Question

Mathematical induction...give the counterexample to disprove the following...1^3+2^3+3^3+...+n^3=n^4-n^3+1....I am lost, please help!

Answer 1

If n =3, that is you use 3 terms from the LHS and replace n =3 on the RHS
\(1^3+2^3+3^3=1+8+27= 36\)
while the RHS is \(3^4-3^3+1=81-27+1=55\)
Hence \(LHS\neq RHS\)

Answer 2

Why use n=3?

Answer 3

Because it is the case, the equation becomes inequality.