# 101st Fibonacci number

Calculating the 101st Fibonacci number without a calculator or programming language can be quite tedious due to the large numbers involved. However, if you're up for the challenge, you can use a method called "iterative Fibonacci sequence generation" which involves systematically generating each Fibonacci number in sequence until you reach the desired index.

Here's how you can do it manually:

Step 1: Initialize Variables

Start with two variables initialized to the first two Fibonacci numbers: F0 = 0 and F1 = 1.

Step 2: Iterate to Generate Fibonacci Numbers

Continue generating Fibonacci numbers iteratively until you reach the desired index (101 in this case). The next Fibonacci number in the sequence is the sum of the previous two Fibonacci numbers.

` F2 = F1 + F0 = 1 + 0 = 1 `

` F3 = F2 + F1 = 1 + 1 = 2 `

` F4 = F3 + F2 = 2 + 1 = 3 `

` F5 = F4 + F3 = 3 + 2 = 5 `

` F6 = F5 + F4 = 5 + 3 = 8 `

` F7 = F6 + F5 = 8 + 5 = 13 `

` F8 = F7 + F6 = 13 + 8 = 21 `

` F9 = F8 + F7 = 21 + 13 = 34 `

` F10 = F9 + F8 = 34 + 21 = 55 `

` F11 = F10 + F9 = 55 + 34 = 89 `

` F12 = F11 + F10 = 89 + 55 = 144 `

` F13 = F12 + F11 = 144 + 89 = 233 `

` F14 = F13 + F12 = 233 + 144 = 377 `

` F15 = F14 + F13 = 377 + 233 = 610 `

` F16 = F15 + F14 = 610 + 377 = 987 `

` F17 = F16 + F15 = 987 + 610 = 1597 `

` F18 = F17 + F16 = 1597 + 987 = 2584 `

` F19 = F18 + F17 = 2584 + 1597 = 4181 `

` F20 = F19 + F18 = 4181 + 2584 = 6765 `

` F21 = F20 + F19 = 6765 + 4181 = 10946 `

` F22 = F21 + F20 = 10946 + 6765 = 17711 `

` F23 = F22 + F21 = 17711 + 10946 = 28657 `

` F24 = F23 + F22 = 28657 + 17711 = 46368 `

` F25 = F24 + F23 = 46368 + 28657 = 75025 `

` F26 = F25 + F24 = 75025 + 46368 = 121393 `

` F27 = F26 + F25 = 121393 + 75025 = 196418 `

` F28 = F27 + F26 = 196418 + 121393 = 317811 `

` F29 = F28 + F27 = 317811 + 196418 = 514229 `

` F30 = F29 + F28 = 514229 + 317811 = 832040 `

` F31 = F30 + F29 = 832040 + 514229 = 1346269 `

` F32 = F31 + F30 = 1346269 + 832040 = 2178309 `

` F33 = F32 + F31 = 2178309 + 1346269 = 3524578 `

` F34 = F33 + F32 = 3524578 + 2178309 = 5702887 `

` F35 = F34 + F33 = 5702887 + 3524578 = 9227465 `

` F36 = F35 + F34 = 9227465 + 5702887 = 14930352 `

` F37 = F36 + F35 = 14930352 + 9227465 = 24157817 `

` F38 = F37 + F36 = 24157817 + 14930352 = 39088169 `

` F39 = F38 + F37 = 39088169 + 24157817 = 63245986 `

` F40 = F39 + F38 = 63245986 + 39088169 = 102334155 `

` F41 = F40 + F39 = 102334155 + 63245986 = 165580141 `

` F42 = F41 + F40 = 165580141 + 102334155 = 267914296 `

` F43 = F42 + F41 = 267914296 + 165580141 = 433494437 `

` F44 = F43 + F42 = 433494437 + 267914296 = 701408733 `

` F45 = F44 + F43 = 701408733 + 433494437 = 1134903170 `

` F46 = F45 + F44 = 1134903170 + 701408733 = 1836311903 `

` F47 = F46 + F45 = 1836311903 + 1134903170 = 2971215073 `

` F48 = F47 + F46 = 2971215073 + 1836311903 = 4807526976 `

` F49 = F48 + F47 = 4807526976 + 2971215073 = 7778742049 `

` F50 = F49 + F48 = 7778742049 + 4807526976 = 12586269025 `

` F51 = F50 + F49 = 12586269025 + 7778742049 = 20365011074 `

` F52 = F51 + F50 = 20365011074 + 12586269025 = 32951280099 `

` F53 = F52 + F51 = 32951280099 + 20365011074 = 53316291173 `

` F54 = F53 + F52 = 53316291173 + 32951280099 = 86267571272 `

` F55 = F54 + F53 = 86267571272 + 53316291173 = 139583862445 `

` F56 = F55 + F54 = 139583862445 + 86267571272 = 225851433717 `

` F57 = F56 + F55 = 225851433717 + 139583862445 = 365435296162 `

` F58 = F57 + F56 = 365435296162 + 225851433717 = 591286729879 `

` F59 = F58 + F57 = 591286729879 + 365435296162 = 956722026041 `

` F60 = F59 + F58 = 956722026041 + 591286729879 = 1548008755920 `

` F61 = F60 + F59 = 1548008755920 + 956722026041 = 2504730781961 `

` F62 = F61 + F60 = 2504730781961 + 1548008755920 = 4052739537881 `

` F63 = F62 + F61 = 4052739537881 + 2504730781961 = 6557470319842 `

` F64 = F63 + F62 = 6557470319842 + 4052739537881 = 10610209857723 `

` F65 = F64 + F63 = 10610209857723 + 6557470319842 = 17167680177565 `

` F66 = F65 + F64 = 17167680177565 + 10610209857723 = 27777890035288 `

` F67 = F66 + F65 = 27777890035288 + 17167680177565 = 44945570212853 `

` F68 = F67 + F66 = 44945570212853 + 27777890035288 = 72723460248141 `

` F69 = F68 + F67 = 72723460248141 + 44945570212853 = 117669030460994 `

` F70 = F69 + F68 = 117669030460994 + 72723460248141 = 190392490709135 `

` F71 = F70 + F69 = 190392490709135 + 117669030460994 = 308061521170129 `

` F72 = F71 + F70 = 308061521170129 + 190392490709135 = 498454011879264 `

` F73 = F72 + F71 = 498454011879264 + 308061521170129 = 806515533049393 `

` F74 = F73 + F72 = 806515533049393 + 498454011879264 = 1304969544928657 `

` F75 = F74 + F73 = 1304969544928657 + 806515533049393 = 2111485077978050 `

` F76 = F75 + F74 = 2111485077978050 + 1304969544928657 = 3416454622906707 `

` F77 = F76 + F75 = 3416454622906707 + 2111485077978050 = 5527939700884757 `

` F78 = F77 + F76 = 5527939700884757 + 3416454622906707 = 8944394323791464 `

` F79 = F78 + F77 = 8944394323791464 + 5527939700884757 = 14472334024676221 `

` F80 = F79 + F78 = 14472334024676221 + 8944394323791464 = 23416728348467685 `

` F81 = F80 + F79 = 23416728348467685 + 14472334024676221 = 37889062373143906 `

` F82 = F81 + F80 = 37889062373143906 + 23416728348467685 = 61305790721611591 `

` F83 = F82 + F81 = 61305790721611591 + 37889062373143906 = 99194853094755497 `

` F84 = F83 + F82 = 99194853094755497 + 61305790721611591 = 160500643816367088 `

` F85 = F84 + F83 = 160500643816367088 + 99194853094755497 = 259695496911122585 `

` F86 = F85 + F84 = 259695496911122585 + 160500643816367088 = 420196140727489673 `

` F87 = F86 + F85 = 420196140727489673 + 259695496911122585 = 679891637638612258 `

` F88 = F87 + F86 = 679891637638612258 + 420196140727489673 = 1100087778366101931 `

` F89 = F88 + F87 = 1100087778366101931 + 679891637638612258 = 1779979416004714189 `

` F90 = F89 + F88 = 1779979416004714189 + 1100087778366101931 = 2880067194370816120 `

` F91 = F90 + F89 = 2880067194370816120 + 1779979416004714189 = 4660046610375530309 `

` F92 = F91 + F90 = 4660046610375530309 + 2880067194370816120 = 7540113804746346429 `

` F93 = F92 + F91 = 7540113804746346429 + 4660046610375530309 = 1.2200160415122E+19 `

` F94 = F93 + F92 = 1.2200160415122E+19 + 7540113804746346429 = 1.9740274219868E+19 `

` F95 = F94 + F93 = 1.9740274219868E+19 + 1.2200160415122E+19 = 3.194043463499E+19 `

` F96 = F95 + F94 = 3.194043463499E+19 + 1.9740274219868E+19 = 5.1680708854858E+19 `

` F97 = F96 + F95 = 5.1680708854858E+19 + 3.194043463499E+19 = 8.3621143489848E+19 `

` F98 = F97 + F96 = 8.3621143489848E+19 + 5.1680708854858E+19 = 1.3530185234471E+20 `

` F99 = F98 + F97 = 1.3530185234471E+20 + 8.3621143489848E+19 = 2.1892299583456E+20 `

` F100 = F99 + F98 = 2.1892299583456E+20 + 1.3530185234471E+20 = 3.5422484817926E+20 `

` F101 = F100 + F99 = 3.5422484817926E+20 + 2.1892299583456E+20 = 5.7314784401382E+20 `

101st Fibonacci number is: 5.7314784401382E+20.

## Sum of the first 101 Fibonacci numbers

`SUMM = F1 + F2 + F3 + F4 + F5 + F6 + F7 + F8 + F9 + F10 + F11 + F12 + F13 + F14 + F15 + F16 + F17 + F18 + F19 + F20 + F21 + F22 + F23 + F24 + F25 + F26 + F27 + F28 + F29 + F30 + F31 + F32 + F33 + F34 + F35 + F36 + F37 + F38 + F39 + F40 + F41 + F42 + F43 + F44 + F45 + F46 + F47 + F48 + F49 + F50 + F51 + F52 + F53 + F54 + F55 + F56 + F57 + F58 + F59 + F60 + F61 + F62 + F63 + F64 + F65 + F66 + F67 + F68 + F69 + F70 + F71 + F72 + F73 + F74 + F75 + F76 + F77 + F78 + F79 + F80 + F81 + F82 + F83 + F84 + F85 + F86 + F87 + F88 + F89 + F90 + F91 + F92 + F93 + F94 + F95 + F96 + F97 + F98 + F99 + F100 + F101 = 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 + 144 + 233 + 377 + 610 + 987 + 1597 + 2584 + 4181 + 6765 + 10946 + 17711 + 28657 + 46368 + 75025 + 121393 + 196418 + 317811 + 514229 + 832040 + 1346269 + 2178309 + 3524578 + 5702887 + 9227465 + 14930352 + 24157817 + 39088169 + 63245986 + 102334155 + 165580141 + 267914296 + 433494437 + 701408733 + 1134903170 + 1836311903 + 2971215073 + 4807526976 + 7778742049 + 12586269025 + 20365011074 + 32951280099 + 53316291173 + 86267571272 + 139583862445 + 225851433717 + 365435296162 + 591286729879 + 956722026041 + 1548008755920 + 2504730781961 + 4052739537881 + 6557470319842 + 10610209857723 + 17167680177565 + 27777890035288 + 44945570212853 + 72723460248141 + 117669030460994 + 190392490709135 + 308061521170129 + 498454011879264 + 806515533049393 + 1304969544928657 + 2111485077978050 + 3416454622906707 + 5527939700884757 + 8944394323791464 + 14472334024676221 + 23416728348467685 + 37889062373143906 + 61305790721611591 + 99194853094755497 + 160500643816367088 + 259695496911122585 + 420196140727489673 + 679891637638612258 + 1100087778366101931 + 1779979416004714189 + 2880067194370816120 + 4660046610375530309 + 7540113804746346429 + 1.2200160415122E+19 + 1.9740274219868E+19 + 3.194043463499E+19 + 5.1680708854858E+19 + 8.3621143489848E+19 + 1.3530185234471E+20 + 2.1892299583456E+20 + 3.5422484817926E+20 + 5.7314784401382E+20 = 1.5005205362069E+21`

Sum of the first 101 Fibonacci numbers: 1.5005205362069E+21.
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