Question

determine whether the infinite geometric series converges or diverges; if it converges calculate its sum

Answer 1

A geometric serie is given by:

$\sum_{k\mathop{=}0}^{\infty}a_1(r)^{k-1}$

Where:

a1 = First term of the sequence = 420

r= common ratio = 0.8

The srie sconverges if and only if:

$\begin{gathered} -1he seris converge asnd its sum is gviven by:

[tex]\sum_{k\mathop{=}1}^{\infty}420(0.8)^{k-1}=\frac{a_1}{1-r}=\frac{420}{1-0.8}=2100$