Find the *n*th partial sum of the series

for

(a) *n* = 1

(b) *n* = 3

(c) *n* = 5

Answer

(a) The 1st partial sum of a series is its first term. In this case, the 1st partial sum is

2(1) = 2.

(b) The 3rd partial sum is the sum of the first 3 terms:

2(1) + 2(2) + 2(3) = 12.

(c) The 5th partial sum is the sum of the first 5 terms:

2(1) + 2(2) + 2(3) + 2(4) + 2(5) = 30.

We usually denote the *n*th partial sum of a series by *S*_{n}.