InterviewSolution
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InterviewSolution
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For all natural numbers n, statementp(n)= 1+2+3+ 4....+n = (n(n+1))/2 is truefind p(n+1) |
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Answer» `(N(n+1))/2` `=1/2 n(n+1)` For n=1 `L.H.S =1` `R.H.S =1/2 .1 (1+1) =1/2 .1.2=1` `L.H.S. =R.H.S` Therefore p (n) is TRUE for n=1 Let P (n) is true for n=K `:. P (K) :1+2+3+….+K =1/2 K(k+1)` Adding(k+1) on both sides `1+2+3+.....+K+(K+1)` `=1/2 K(k+1) +(K+1)` `=1/2 (K+1) (K+2)` `=1/2 (K+1){(K+1)+1}` `rArr ""P (n)" is also true for" n=K +1 ` Hence by the principle of mathematical induction, GIVEN STATEMENT is true for all natural NUMBER 'n' |
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