Question

For what value(s) of r is the series the summation from n=1 to infinity of 1/n^r+1 convergent?
a) r > -2
b) r > -1
c) r ≥ -2
d) All values of r

Answer 1

do you mean 1/n^(r+1)

well d is just plain out
1/n^(-100 + 1 ) gets big

if r = -2
looks like
1/ n^(-2 + 1) = n hardly

if r = -1
1/ (n^0) = 1 that works and so does any bigger r

Answer 2

Sorry it was my fault. The question is: For what value(s) of r is the series the summation from n=1 to infinity of 1/(n^r+3) convergent?