Question

Makeaconjectureforthenextequationandverifyit.Hint:TheFibonacciSequenceisusedhere.1 = 2 − 11 + 1 = 3 − 11 + 1 + 2 = 5 − 11 + 1 + 2 + 3 = 8 − 11 + 1 + 2 + 3 + 5 = 13 − 1

Answer 1

The fibonacci sequence is a sequence in which each element of the sequence is the sum of the two previous numbers.

The sequence stars with 0 and 1:

0+1=1

then 1 and 1

1+1 =2

then 1 and 2:

1+2=3

then 3 and 2:

3+2=5

and so on...

As we can see, this sequence follows the form of the fibonacci sequence: 2, 3, 5, 8, 13 But substracting -1 to it.