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Numerade Educator

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Problem 79 Hard Difficulty

Find the sum of the series.

$ 3 + \frac {9}{2!} + \frac {27}{3!} + \frac {81}{4!} + \cdot \cdot \cdot $

Answer

$e^{3}-1$

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Video Transcript

okay, It's a funnel. Some of the series three plus nine over to Victoria Pass 73 over. Victoria plus 81 over Victoria. All right, so we can rewrite this as 3/1 pictorial plus three square or pictorial plus three cube or thrift for you. Plus 3 to 4 over. Prosecutorial plus three to the end over in Victoria. So which is just so three to the n, our in tutorial and any is from one to infinity. And this is rather familiar of us because we recall that into the X It's into the X, which is exponential function of X, which is equals two X to the in, over in Victoria and AIDS from zero to infinity. But here is from one to infinity. So this is equals two. And from zero to infinity. 3 to 0 in no, in factorial minus one. So this part will be simplified to eight. Cute cube, and we just minus one. So the result is gonna be a Q minus one. All right,