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

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asked May 20, 2023 73.5k views

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Sockmonk · Answer 1 · 2023-05-24T20:36:47+0000

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:

$\begin{gathered} -1he seris converge asnd its sum is gviven by:<p></p>[tex]\sum_{k\mathop{=}1}^(\infty)420(0.8)^(k-1)=(a_1)/(1-r)=(420)/(1-0.8)=2100$

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

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