# Convergent or divergent series

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Please assist with the following problems I am having a hard time solving. Please see attached.

Determine if the following series are convergent or divergent

Find the values of x for which

and tell if the series converges or diverges when given the series

Find power series for the following functions

Write down the first 4 Taylor polynomials around zero and plot f(x) a long with its approximation

f(x)=e^(2x+1)

Use the integral test to determine if the series converges or diverges

∑_(k=1)^∞▒〖1/2k-〗 1/(2k+1)

Use the comparison test test to determine if the series converges or diverges

∑_(k=1)^∞▒1/(2k^4+8)

EVALUATE THE INTEGRALS. USE TRIG SUBSTITUTION AND SHOW WORK

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This posting explains different methods of testing convergent or divergent series.

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Hi,

Please find detailed solution attached herewith. I hope it will help you.

I will be happy to assist you in future.

Thanks

1. Determine if the following series are convergent or divergent

Solution:

Thus, the series converges.

2. Find the values of x for which

and tell if the series converges or diverges when given the series

Solution:

L < ...

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