use mathematical induction to prove that 1^3+2^3+3^3+...+n3=(n(n+1)/2)^2 for all positive integers
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To prove using Principal of Mathematical Induction,
Let assume that ,
Step :- 1 For n = 1
Step :- 2 Let assume that P(n) is true for n = k, where k is some natural number.
Step :- 3 We have to prove that P(n) is true for n = k + 1
Consider LHS
On substituting the value from step 2, we get
Hence, By the Process of Principal of Mathematical Induction,
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