How do you find general term formula for {-1/4, 2/9, -3/16, 4/25, ...}?

1 Answer
Mar 24, 2016

Answer:

#n^(th)# term of the series #{-1/4, 2/9, -3/16, 4/25, ...}# is#((-1)^nxxn)/(n+1)^2#

Explanation:

Here one desires is the #n^(th)# term of the series #{-1/4, 2/9, -3/16, 4/25, ...}#.

As is observed the numerators are #{-1, 2, -3, 4, ...}#. Hence numerator of #n^(th)# term is #n# if #n# is odd and #-n# if #n# is even.

Hence we can write numerator of #n^(th)# term as #(-1)^nxxn#.

The denominators are #{4,9,16,25,...}# i.e. #n^(th)# term is the square of #(n+1)# or #(n+1)^2#.

Hence general formula for #n^(th)# term of the series #{-1/4, 2/9, -3/16, 4/25, ...}# is #((-1)^nxxn)/(n+1)^2#