1^3+2^3+3^3+4^3+5^3+...+30^3=

Question

this is an arithmetic progression question i guess... but can't solve it with arithmetic progression formula.

Answer 1

Question: 1^3+2^3+3^3+4^3+5^3+...+30^3= ?

This is the sum of the cubes (of integers) and is given by a summation formula.

An easier way to remember the formula is:

The sum of the cubes (of integers) is equal to the square of the sum (of integers).

We have: ∑[k=1 to n] (k) = n(n+1)/2

Hence

∑[k=1 to n] (k^3) = {n(n+1)/2}^2

Te evaluate 1^3+2^3+3^3+4^3+5^3+...+30^3, it is simjpler to work out S = 1+2+3+4+5+...+30, and then square it.

S = ∑[k=1 to 30] (k) = 30(31)/2 = 930/2 = 465

S^2 = 465^2 = 216,225

Hence, 1^3+2^3+3^3+4^3+5^3+...+30^3 = 216,225