Sum to n terms of 1, (4-a)x, (7-a^2)x^2, (10-a^3)x^3

[Procrastinate]

I just had this question on my exam and I was wondering whether my method of calculating it was right:

I was meant to find sum to n terms of this:

1, (4-a)x, (7-a^2)x^2, (10-a^3)x^3, (13-a^4)x^4...

Would the correct way to go about it be expand it:

1, 4x-ax. 7x^2-a^2x^2...

and then it would be:

Sn = (power series of 1, 4x, 7x^2...) - ax(1-ax^(n-1)/(1-ax)

 

[tiny-tim]

Hi Procrastinate!

(try using the X² tag just above the Reply box )

The first thing to do with any question like this (in my opinion, anyway) is to write it logically …

it's ∑ (3n + 1 - aⁿ)xⁿ

= ∑ xⁿ + 3∑ nxⁿ - ∑(ax)ⁿ …