Question

If 1 + 2 + 4 + 8 + ......... n terms = 255, then the value of n is​

Answer 1

Answer:

Given:

1+2+4+8+ .... 2n = 255

This series is a geometric progression, hence we can use the sum of geometric progression to n terms to find the answer.

a=1 ; r = 2

Sn = a(r^n-1)/(r-1)

255 = 1(2^2n - 1)/(2-1)

» 255 = 4^n - 1

» 256 = 4^n

» n = 4