60th Fibonacci number
Calculating the 60th 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:
Start with two variables initialized to the first two Fibonacci numbers: F0 = 0 and F1 = 1.
Continue generating Fibonacci numbers iteratively until you reach the desired index (60 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
Sum of the first 60 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 = 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 = 4052739537880