Determine whether the series is convergent or divergent by expressing sn as a telescoping sum. [infinity]
Σ 8/n^2-1
n=3

The sum converges at:

Step-by-step explanation:

Given

Express the denominator as difference of two squares

Express 8 as 4 * 2

Rewrite as:

Express 2 as 1 + 1 + 0

Express 0 as n - n

Rewrite as:

Split

Cancel out like terms

In the above statement, we have:

Add

Notice that the pattern follows:

The above represent the odd sums (say S1)

For the even sums, we have:

In the above statement, we have:

Add to both sides

Notice that the pattern follows:

The above represent the even sums (say S2)

The total sum (S) is:

Remove all k terms

Open bracket

The sum converges at: