# Calculus

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.

## Similar Questions

1. ### Calculus

For what values of p>0 does the series Riemann Sum [n=1 to infinity] 1/ [n(ln n) (ln(ln n))^p] converge and for what values does it diverge?
2. ### Calculus

If you have a geometric alternating series, and you prove that the series is converging by doing geometric series test, and NOT alternating series test, then does that allow you to say that the series converges ABSOLUTELY?
3. ### Calculus

The problem with these two questions is that I cannot determine the a and r. The 3rd question-I don't know what I did wrong. Thanks for the help! Tell whether the series converges or diverges. If it converges, give its sum. infinity …
4. ### calculus

determine whether the series converges of diverges the sum from n=1 to infinity of 1/(the square root of (n^3+1)) I said that through the comparision test (comparing to 1/the square root of (n^3) the series converges
5. ### calculus

determine whether the series converges of diverges the sum from n=1 to infinity of 1/(the square root of (n^3+1)) I said that through the comparision test (comparing to 1/the square root of (n^3) the series converges is this true?
6. ### College Calculus

Suppose the series An (from n=1 to INF) is known to be convergent. Prove that series 1/(An) (from n=1 to INF) is a divergent series. I have no idea what to do... please help!
7. ### Calculus

Determine the following about the series. Indicate the test that was used and justify your answer. Sigma (lower index n = 1; upper index infinity) [sin((2n-1)pi/2)]/n A. The series diverges B. The series converges conditionally. C. …
8. ### Calculus

How do I figure out if the series from 3 to inf of ((1/2)^(n+1))((2/3)^n) converges or diverges?
9. ### Calculus

Use the ratio test to find whether the series diverges or converges. 1/5^n (1 to infinity) I think the limit converges to 1/5, so the series converges.
10. ### Calculus

Determine whether the series from 0 to infinity of cos(nπ)/(n + 3) converges conditionally or absolutely. A. The series diverges. B. The series converges conditionally but not absolutely. C. The series converges absolutely but not …

More Similar Questions