Using mathematical induction prove that for all positive integers n.


To prove : P(n) : = nxn – 1 for all positive integers n


For n = 1,


LHS = = 1


RHS = 1 × x1 – 1 = 1


So, LHS = RHS


P(1) is true.


P(n) is true for n = 1


Let P(k) be true for some positive integer k.


i.e. P(k) =


Now, to prove that P(k + 1) is also true


RHS = (k + 1)x(k + 1) – 1


LHS =







LHS = RHS


Thus, P(k + 1) is true whenever P(k) is true.


Therefore, by the principle of mathematical induction, the statement P(n) is true for every positive integer n.


Hence, proved.


19
1