First slide
Introduction to P.M.I

The identity 13+23+33++n3 is equal to


Let the given statement be P(n).


Step I : For n=1,

             P(1):1(1+1)22=1×222=12=1=13 which is true

Step ll: Let it is true for n = k, 


Step lll: For n=k+1,


           =k(k+1)22+(k+1)3      [using Eq. (i)] 


  On taking (k + 1)2 common in numerator Part, 


Therefore, P(k + 1) is true when P(k) is true. 

Hence, from the principle of mathematical induction, the statement is true for all natural numbers n.

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