Use the "summation formulas" to express the following sum in closed form. Your answer should be in terms of n.

Question

n

∑(3+4k)^2

k=1

Answer 1

Expand the summand: 9 + 24k + 16k²

Then you will need 3 formulae:

∑9 from k = 1 to n = 9n

∑k from k = 1 to n = n(n+1)/2

∑k² from k = 1 to n = n(n+1)(2n+1)/6

It is not difficult to derive these formulae and if you want/need the derivation, please make a comment to that effect and I will try to help.

Added 5:17 PM

What you need is:

9n + 24n(n+1)/2 + 16n(n+1)(2n+1)/6

Now expand the terms and collect like terms.

You will get a cubic polynomial, which is what you are looking for.

Note: The expression I wrote satisfies the question, i.e. it is a closed form in n,

but what you want is a polynomial in n.)