Conclude-the-value-of-the-sum-S-n-n-0-2-n-1-2-n-n-n-with-help-of-1-2x-n-

Question Number 178530 by Acem last updated on 17/Oct/22

C o n c l u d e t h e v a l u e o f t h e s u m :

S_{n} = (\begin{matrix} n \\ 0 \end{matrix}) + 2 (\begin{matrix} n \\ 1 \end{matrix}) + \dots + 2^{n} (\begin{matrix} n \\ n \end{matrix})

w i t h h e l p o f {(1 + 2 x)}^{n}

Answered by Ar Brandon last updated on 17/Oct/22

S = \underset{k = 0}{\sum^{n}} \overset{n}{} C_{k} 2^{k} = {(2 + 1)}^{n} = 3^{n}

\underset{k = 0}{\sum^{n}} \overset{n}{} C_{k} a^{k} b^{n - k} = {(a + b)}^{n}

Commented by Acem last updated on 17/Oct/22

G r e a t S i r!

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