Proof by Math Induction
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Prove
1^3 + 2^3 + ......+ n^3 = (1 + 2 + ..... n)^2 for all natural numbers n.
I have not done ones where the right hand side looks like this one does.
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The expert provides an induction mathematical proof. A complete, neat and step-by-step solution is provided in the attached file.
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Prove
1^3 + 2^3 + ......+ n^3 = (1 + 2 + ..... n)^2 for all natural numbers n.
Step # LHS RHS
To Prove 1^3 + 2^3 + ... + n^3 (1 + 2 + ... + n)^2
= [n(n + 1)/2]^2
1 Put n = 1. Then 1^3 = 1 [1(1 + 1)/2]^2 = 1
2 Put n = 2. Then 1^3 + 2^3 = 9 [2(2 + 1)/2]^2 = 0
3 From (1) and (2) we see that the theorem is true for n = 1 and for n = 2
4 Let the theorem be true for n ...
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