prove using mathematical induction

Asked by  | 30th Sep, 2008, 08:32: PM

Expert Answer:

for n=1 then L.H.S. = 1 and R.H.S. = 1(1+1)/2 = 1

which is true for n=1

now for n=2 , L.H.S. = 1+2=3 and R.H.S. = 2(2+1)/2 = 3

which is also true.

now let this is true for n=N i.e. for n=N

1+2+3+.....+N = N(N+1)/2

now we have to prove that this is true for n=N+1

L.H.S = sum of N terms + (N+1)th term

= N(N+1)/2 + (N+1)

=(N+1)(N/2+1)

= (N+1)(N+2)/2

and in R.H.S put n=N+1

so R.H.S. = (N+1)(N+2)/2

since L.H.S. = R.H.S.

hence proved.

 

Answered by  | 30th Sep, 2008, 08:47: PM

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