Find the sum of the following series sum_{k=2}^infty(-1)^kfrac{3}{2^{3k}}

Tobias Ali

Tobias Ali

Answered question

2021-02-05

Find the sum of the following series
k=2(1)k323k

Answer & Explanation

Lacey-May Snyder

Lacey-May Snyder

Skilled2021-02-06Added 88 answers

Given:
k=2(1)k323k Solution: k=2(1)k323k
=3k=2(1)k23k
=3k=2(123)k
=3k=2(18)k
The sum is a geometric series with the first term =(18)2 and common ratio =(18)
So we can use the infinite geometric series sum formula for this
Using the formula we get
=3(18)21(18)=316498=3×164×89=124
Answer: 124

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