Question

If the nth partial sum of a series is Sₙ, find an expression for Sₙ.

Answer 1

The expression for the nth partial sum of a series is found by evaluating the sum of the first n terms of the series.

Step-by-step explanation:

The expression for the nth partial sum of a series can be found by evaluating the sum of the first n terms of the series. Let's say the terms of the series are represented by the sequence a_1, a_2, a_3, ..., a_n. The nth partial sum, S_n, can be expressed as:

S_n = a_1 + a_2 + a_3 + ... + a_n

For example, if we have the series 1, 3, 5, 7, 9, ..., the nth term can be expressed as a_n = 2n - 1. So the nth partial sum would be:

S_n = (2(1) - 1) + (2(2) - 1) + (2(3) - 1) + ... + (2(n) - 1)