Use the Integral Test to determine whether the infinite series is convergent. ∑n=1∞12ne−n2
Fill in the corresponding integrand and the value of the improper integral.

You are correct that the series converges, but the integral you use in the test should contain x in place of n, since you're integrating with respect to x.

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!