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**Converting Sigma notation....**

## Homework Statement

(Not a homework question)

Hi!!

I have been encountering problems in Binomial Theorem which includes converting the sigma notation.

Like [tex]\sum_{k=0}^n \frac{n!}{(n-k)!k!} a^kb^{n-k}=(a+b)^n[/tex]

I got many questions in my exam of this type with four options.

One of them was:-

[tex]\sum_{k=1}^{n} {}^nC_k.3^k[/tex]

I substituted the value of n and was able to figure out the correct option.

But as i said there were many questions, so it took a lot of time.

Is there any easier way to do that?

## Homework Equations

## The Attempt at a Solution

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