Question

[Nguyễn Thành Hưng]

Your school is having a canned food drive for Harvesters. How many total cans would you have if you made a solid pyramid with $15\times 15$ cans on the first level, $14\times 14$ on the second level and continue the pattern all the way up to just one can on top?
Answer:

cans.

Answer 1

[Đoàn Đức Hà]

We need to find the value of the expression: 

\(15^2+14^2+...+2^2+1^2\).

We have general formula for the sum of a sequence: \(1^2+2^2+...+n^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}\).

\(15^2+14^2+...+2^2+1^2=\frac{15\left(15+1\right)\left(2.15+1\right)}{6}=1240\)