for n=1 to infinity, does the series of 7/n(n+2) converge

Only when n = Nissan

No, because as n increases 7/n(n+2) decreases.

Is this a quiz to get a job as an Infiniti salesman?

Yes, the series converges. Use the Integral Convergence Test and sort the integral out by using partial fractions.

A/N + B/(N+2) = 7/n(N+2)

A(n+2) + B(N) = 7

Set n= 0 to solve for A ==> A(2) +0 = 7 [A=7/2)
Set n=(-2) to solve for B ==> B(-2) = 7 [B=-7/2]
then integrate both (you will be using ln for your integral. Combine ln later on and you're set. It will yield a number, which means it convergences. hense the series must converge.

yup -it converges. size of divisor get bigger as series progress. but what does that have to do with the infiniti make of cars. your in the wrong area !!! ( answer is valid tho :) )