Question

Prove that Sn=n(n+1) for the sequence an=2n,where n is any positive integers​

Answer 1

Proved

Explanation:

Given

`a_n = 2n`

Required

Prove that
`S_n = n(n+1)`

The given sequence is an arithmetic sequence.

The Sn of this sequence is:

`S_n = (n)/(2)(a_1 + a_n)`

Calculate a1

`a_n =2n`

`a_1 =2*1`

`a_1 =2`

So, we have:

`S_n = (n)/(2)(a_1 + a_n)`

`S_n = (n)/(2)(2 + 2n)`

Factor out 2

`S_n = (n*2)/(2)(1 + n)`

`S_n = n(1 + n)`

`S_n = n(n + 1)` --- Proved