Question

Use the Integral Test to determine whether the series is convergent or divergent given ∑1n5

from n=1 to infinity?

Answer 1

What is the Integral Test?

The integral test is used to find whether the given series is converged or not. The convergence of series is more significant in many situations when the integral function has the sum of a series of functions.

Solving the problem

∫1+∞f(x)dx exists finite ⇒ ∑+∞ (n=1) an coverges.

we know ∫1+∞ 1/x^5dx= (-1/4x^4)1+∞ = 1/4, which is finite, so the series converges.

(If this is wrong you have every right to report me)

I hoped this helped <3333