How do you use the integral test to determine the convergence or divergence of #Sigma 1/n^2# from #[1,oo)#?
1 Answer
Dec 22, 2016
The series
Explanation:
The integral test states that, given:
if we have a function
(i)....
#f(x)# is positive
(ii)...#f(x)# is decreasing
(iii)#lim_(x->+oo) f(x) = 0#
(iv)...#f(n) = a_n#
then a necessary and sufficient condition for the series above to converge is that the integral:
converges as well.
It's easy to see that for the series:
the function
so that the series must be convergent as well.