For each series,( Sum of n+1 to infinity ) find the value of the common ratio, r

ID: 3346092 • Letter: F

Question

so it can be compared to the form; sum of n=1 to infinity of n^k*r^n

How can any of the following be compared to the form of n^k*r^n, where k is a constant?

1.(4+n(7^n))^-7

2.n(pi)*5^(2n)/(5^n + n^9)

3.(N^6 + 8)/(n^7 + 9)

4. [(8(n^2)+7n + 3^-2n)/7^(n+5) + 7n + 5(n^1/2))]

I don't understand how to do these. But I know that if r<1, we get convergence , r>1 divergence, and r=1 p-series.

For my understanding, I need detailed step by step of how to do these problems.

too less time!

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