Simplify-k-0-n-1-3-k-2-n-k-

Question Number 171307 by Raxreedoroid last updated on 12/Jun/22

Simplify

\underset{k = 0}{\sum^{n - 1}} 3^{k} 2^{n - k}

Commented by mr W last updated on 12/Jun/22

= 2^{n} \underset{k = 0}{\sum^{n - 1}} {(\frac{3}{2})}^{k}

= 2^{n} \times \frac{{(\frac{3}{2})}^{n} - 1}{\frac{3}{2} - 1}

= 2 (3^{n} - 2^{n})

Answered by JDamian last updated on 12/Jun/22

2^{n} \underset{k = 0}{\sum^{n - 1}} {(\frac{3}{2})}^{k}

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