Prove that?

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Answer 1 · 2018-03-25T21:41:14

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.