Mathematics: By recognizing the series below as a taylor series evaluated at a particular value of x, find the exact sum of the convergent series. 1 + 3/1! + 9/2! + 27/3! + 81/4! + + 3n/n! +

By recognizing the series below as a taylor series

helphelp81

10.01.2022

e^3

Step-by-step explanation:

Given is a series as

$1+\frac{3}{1!} +\frac{3^2}{2!} +...+\frac{3^n}{n!} +...$

Recall the expansion of

$e^x = 1+x+\frac{x^2}{2!} +...+\frac{x^n}{n!} +...$

This expansion is valid for all real values of x.

Comparing this with our series we find that x =3

Hence the given series = e^3

Thus we find that the given series can be recognized with the expansion of exponential series with powers of e and here we see that power of e is 3.

So the given Taylor series is equivalent to

e^3

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iamthepantaloon8357

14.10.2021

-11/16

Step-by-step explanation:

1 1/8 + b≥ 7/16

-18/16 -18/16

b≥-11/16

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