Question

determine whether the series is convergent if so find sum:

the sum of x=3 to infinity of
(k+1)^2/((x-1)(x-2))

is it infinity meaning it diverges?

Answer 1

x^2 + 2 x + 1
-------------
x^2 - 3 x + 2

divide top and bottom by x^2

1 + 2/x + 1/x^2
-----------------
1 - 3/x + 2/x^2

terms approach 1, not zero as x gets big.