Power Series Convergence for (5^n)(x-2)^n/8n^7: Explained with Ratio Test

[cue928]

For the following power series: n=1 to infinity [(5^n)(x-2)^n]/8n^7
I used the ratio test, which I understand, but why does the book say it is convergent for
5|x-2|<7? I had 5|x-2|<1, but I don't understand why it would say 7?

 

[Dick]

It would be 5|x-2|<7 if it were 7^n in the denominator instead of x^7. Probably a typo in either the question or the answer.