Geometric Sequence

Question

Write the first 4 terms of the geometric series given by

Sum = 1/ (1+4x)

Answer 1

The sum of the geometric sequence ∑_{(n=0 to infinity)} arⁿ is a / (1-r), as long as -1 < r < 1

So, we need to rewrite 1 / (1+4x) in the form a / (1-r).

1 / (1+4x) = 1 / [1 - (-4x)] So, a = 1 and r = -4x (the series converges when -1 < -4x < 1)

The geometric series with sum 1 / (1+4x) is ∑_{(n=0 to infinity)} (1)(-4x)ⁿ = ∑_{(n=0 to infinity)} (--4)ⁿxⁿ, where -1/4<x<1/4