Question

For what value(s) of r is the series the summation from n equals 1 to infinity of the quotient of 1 and n raised to the quantity r plus 4 power convergent? (10 points)

A) All values of r
B) r > -1
C) r ≥ -3
D) r > -3

Answer 1

this is again the Riemann zeta function ∑1/n^p

which converges for p>1
so you just need r+4 > 1