What is the sum of the first 50 numbers of Fibonacci numbers?

Please show me how to get the answer.





~ Thanks.What is the sum of the first 50 numbers of Fibonacci numbers?
Let's list out the first 10 or so terms of the Fibonnaci Sequence:





1 1 2 3 5 8 13 21 34 55 89...





The sums of the first n numbers (Sn) are:


S1 = 1 [The sum of the first term is 1]


S2 = 2 [The sum of the first 2 terms is 2]


S3 = 4 [The sum of the first 3 terms is 4]


S4 = 7 [etc...]


S5 = 12


S6 = 20





Pretty quickly we see that the sum of the first n numbers is actually 1 less than the number 2 terms ahead of that number. For example:





S5 [the sum of the first 5 terms] is 12, which is 1 less than the 7th term [13 - 1]





So to solve your problem, S50, all we need to do is find the 52nd term of the Fibonnaci Sequence and subtract one from it. This happens to be easier said than done, but you can use any search engine to find a list of Fibonnaci numbers.





Simply for the sake of brevity, the 52nd term is 32951280099. Therefore, S50 [the sum of the first 50 Fibonnaci numbers] is 32951280099 - 1 = 32951280098What is the sum of the first 50 numbers of Fibonacci numbers?
The sum of the first n Fibonacci numbers is the (n + 2)nd Fibonacci number minus 1.





so the sum of the first 50 Fibonacci numbers is 52nd Fibonacci number minus 1:


the 52nd Fibonacci number is: 32951280099


32951280099 - 1 = 32951280098 %26lt;%26lt;%26lt;%26lt;%26lt;%26lt;===== ANSWER
The sum of the first 50 numbers is the 52th Fibonacci number minus 1:





32951280099 -1 = 32951280098
that must be one less than the 52nd fibonacci number. ^_^

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