Thursday

February 26, 2015

February 26, 2015

Posted by **Lisa** on Monday, July 29, 2013 at 10:34am.

(x^3)* (e^(-x^4))

Does it converge or diverge and use the integral test to show how. I got that it diverges, but this isn't correct. Can someone please explain? Thanks.

- Calculus-Series -
**MathMate**, Monday, July 29, 2013 at 11:08amI assume the expression is

(n^3)* (e^(-n^4)) for n=1 to +&inf;

You can use the ratio test to show that it converges, namely, show that

a_{n+1}/a_{n}< 1 ∀ k≥1.

The integral test will result in a definite integral from 1 to +&inf; which is not an elementary function, but evaluates numerically to about 0.09. However, this still shows that the series is convergent.

- Calculus-Series -
**Count Iblis**, Monday, July 29, 2013 at 11:39amIntegral from 1 to infinity of

(x^3)* (e^(-x^4)) dx =

1/4 exp(-1)

**Answer this Question**

**Related Questions**

Calculus - For what values of p>0 does the series Riemann Sum [n=1 to ...

Calc - Does 1/ln(x+1) converge or diverge? I've tried the nth term test, limit ...

calculus - Does the series from 0 to infinity of [1/square root of (n+4)] x cos(...

Calculus 2 - n=1 series to infinity (-5^n)/n^3 does it absolutely converge, ...

Calculus - Does the series (1+sin(n))/(10^n) from summation 0 to positive ...

Calculus - determine whether the series converges or diverges. I am stuck on ...

MATH - does the series 1/n from n=0 to infinity converge or diverge? what ...

Calculus - does the series 1/(n^2+n) converge or diverge? n=2 to n=infinity

Calculus - Determine the following about the series. Indicate the test that was ...

calculus please help - the actual problem is integral(2 to +infinity) (1/x^2) dx...