Binomial theorem/Pascal's identity help

Moistwh

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Mar 16, 2019
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Hi I have no idea how to evaluate this sum
1569530967774.png
I know I either have to change the sum or change the binomial coefficient, but Pascal's identity only alters it by 1, not by i.
 
Hi I have no idea how to evaluate this sum
View attachment 13868
I know I either have to change the sum or change the binomial coefficient, but Pascal's identity only alters it by 1, not by i.
\(\displaystyle \sum\limits_{k = 0}^n \binom{n}{k}3^{-k}=\left(1+\dfrac{1}{3}\right)^n\)
 
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