# Help with summation question?

I have a problem involving sums:

I just have no idea how to solve this.

I know how to solve sums but this does not make sense to me. I need the value of the 'a' but in the first one, 'a' must be 9/8 and it must be something else in the second, so forth...

So I cannot solve it...

How do I go about solving this?

Thanks

Recall that $$(1+a_i)^3 = 1 + 3a_i + 3 a_i^2 + a_i^3$$ Hence, $$\sum_{i=1}^{15}(1+a_i)^3 = \sum_{i=1}^{15}1 + 3\sum_{i=1}^{15}a_i + 3 \sum_{i=1}^{15}a_i^2 + \sum_{i=1}^{15}a_i^3$$ This gives us $$\sum_{i=1}^{15}a_i^2 = \dfrac{\displaystyle \sum_{i=1}^{15}(1+a_i)^3 - \displaystyle \sum_{i=1}^{15}1 - 3\displaystyle \sum_{i=1}^{15}a_i - \displaystyle \sum_{i=1}^{15}a_i^3}3$$ I assume you can complete it from here.

Hint: $$(1+a_i)^3=1+3a_i+3a_i^2+a_i^3.$$