# SOLUTION: Use the principle of mathematical induction to prove the following identity. If n is greator and equal to 1 then, 1*2+.......+n(n+1) = (n(n+1)(n+2))/3

Algebra ->  Algebra  -> Distributive-associative-commutative-properties -> SOLUTION: Use the principle of mathematical induction to prove the following identity. If n is greator and equal to 1 then, 1*2+.......+n(n+1) = (n(n+1)(n+2))/3      Log On

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 Question 26478: Use the principle of mathematical induction to prove the following identity. If n is greator and equal to 1 then, 1*2+.......+n(n+1) = (n(n+1)(n+2))/3Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!1*2+.......+n(n+1) = (n(n+1)(n+2))/3 IN INDUCTION ,WE FIRST TEST WHETHER IT IS CORRECT FOR N=1 LHS=1*2=2 RHS=1*2*3/3=2...LHS=RHS...SO IT IS TRUE FOR N=1 NOW WE ASSUME IT IS TRUE FOR N=K ......SOME VALUE...SO 1*2+.......+K(K+1) = (K(K+1)(K+2))/3........................I WE NOW GO ON TO PROVE THAT IT IS TRUE FOR N=K+1...THAT IS...TPT 1*2+.......+K(K+1)+(K+1)(K+2) = ((K+1)(K+2)(K+3))/3..........II LHS={1*2+.......+K(K+1)}+(K+1)(K+2)...USING EQN.I =(K(K+1)(K+2))/3}+(K+1)(K+2) =(K+1)(K+2){(K/3)+1} =(K+1)(K+2){(K+3)/3} =((K+1)(K+2)(K+3))/3=RHS OF EQN.II. SO WE GOT IT NOW THAT ,IF THE GIVEN RELATION IS TRUE FOR N=K,THEN IT IS TRUE FOR N=K+1 BUT WE PROVED FIRST THAT IT IS TRUE FOR N=1 SO IT IS TRUE FOR N=2 SO IT IS TRUE FOR N=3 SO IT IS TRUE FOR N=4 ........ETC.......... SO IT IS TRUE FOR ALL INTEGRAL VALUES OF N