posted by Anonymous
If the series from n=1 to infinity of n^P converges, then which of the following is false?
a. P < 1
b. the series from n=1 to inf of n^-P converges
c. the integral from n=1 to inf of x^P dx is finite
d. the integral from n=1 to inf of x^(P-1) dx is finite
e. the integral from n=1 to inf of x^(P-2) dx is finite
I think the answer is b, because P must be less than -1 to converge, and -P would just be a positive P that would lead the series to diverge.