Question

Prove that?

Answer 1

We seek:

`S = sum_(i=1)^n (2i-4)`

We can utilise the standard summation formula:

`sum_(i=1)^n i = 1/2n(n+1)`

And so we get:

`S = 2 \ sum_(i=1)^n i- sum_(i=1)^n 4`

`\ \ = 2 * 1/2n(n+1) - 4n`

`\ \ = n(n+1) - 4n`

`\ \ = n^2+n - 4n`

`\ \ = n^2- 3n`

And we can draw an appropriate conclusion.