SOLUTION: Consider the sum 1^3+2^3+3^3+...+n^3 and the sum 1+2+3+...+n. Conjecture a formula that relates these two sums.

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Question 28680: Consider the sum 1^3+2^3+3^3+...+n^3 and the sum 1+2+3+...+n. Conjecture a formula that relates these two sums.
Answer by venugopalramana(3286) About Me  (Show Source):
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Consider the sum 1^3+2^3+3^3+...+n^3 and the sum 1+2+3+...+n. Conjecture a formula that relates these two sums.
S3N = 1^3+2^3+3^3+...+n^3={N(N+1)/2}^2
and S= 1+2+3+...+n. =N(N+1)/2
TRUST YOU ARE TAUGHT THESE FORMULAE.OTHERWISE PLEASE COME BACK AND I SHALL SHOW YOU HOW TO GO ABOUT THEM.
Conjecture a formula that relates these two sums.
HENCE S3N=(SN)^2