Find the interval of convergence for the given series. \\(\\sum_{n=0}^{\\infty}

Question

Find the interval of convergence for the given series.

(sum_{n=0}^{infty} ((-8)^n (x-7)^n)/(5n+3)^{2n} )

Can someone please work this through for me and show every step. The place I get confused is the denominator. I do not know how to handle the fact that there is an "n" value in both power and the portion being raised to that power.

If i try to use the ratio test I end up with

((-8)(x-7)(5n+3)^{2n} / (5n+8)^{2n+2} )

If I use the root test I end up with :

((-8)|x-7| / (5n+3)^2)

Not sure what to do here....  I dont think I can take a limit until the "n" values are eliminated from the problem

Explanation / Answer

u are doing mistake in ratio test

using ratio test :;

tn+1/tn = (-8)(x-7)/(5n+3)^2

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