1
$\begingroup$

I have a problem involving sums:

enter image description here

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

$\endgroup$
4
$\begingroup$

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.

$\endgroup$
1
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.