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Evaluate the infinite geometric series: 13+16+112+124

 May 2, 2022
 #1
avatar+9675 
+5

First term is 1/3.

Common ratio is (1/6)/(1/3) = 1/2.

 

Using the formula sum = a/(1 - r), sum = 13112=23

 May 2, 2022
edited by MaxWong  May 2, 2022
 #2
avatar+70 
+3

Thanks so much!

@MaxWong and @Anthrax

wink

ItsFree  May 2, 2022
edited by ItsFree  May 2, 2022
 #3
avatar+149 
+4

Observe that we can say

13+16+112+=13(1+12+14+)=13n=0(12)n.

Given this, our common ratio r is r=12. Then, by the well-known infinite geometric series formula, we have

13n=0(12)n=131112=23.

 May 2, 2022

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