Find the sum of the convergent series. sum_{n=0}^infty5(frac23)^n

Khadija Wells 2021-02-15 Answered
Find the sum of the convergent series.
n=05(23)n
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Expert Answer

toroztatG
Answered 2021-02-16 Author has 98 answers
To find the sum of the convergent series: n=05(23)n
Solution:
Expanding the given series, we get
n=05(23)n=5(23)1+5(23)2+5(23)3+...
=5[(23)1+(23)2+(23)3+...]
Now, taking the series (23)1+(23)2+(23)3+...
Here,we can find that sequence is in geometric progression.
First term is a1=23
Common ratio is:
r=(23)2(23)
=23
Sum of infinite terms of G.P. is given as:
S=a11r
Sum of the sequence (23)1+(23)2+(23)3+... will be:
S=23123
=2313
=2
Now, sum of the series n=05(23)n will be:
n=05(23)n=5[(23)1+(23)2+(23)3+...]
=52
=10
Hence, required sum is 10.
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Jeffrey Jordon
Answered 2021-12-27 Author has 2047 answers

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