SOLUTION: Conjecture a formula for 1*2+2*3+3*4+....n(n+1).

SOLUTION: Conjecture a formula for 12+23+3*4+....n(n+1).

Question 28617: Conjecture a formula for 1*2+2*3+3*4+....n(n+1).

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
conjecturea formula for 1*2+2*3+3*4+...+n(n+1)=SN
SN=SIGMA{N(N+1)}=SIGMA(N^2)+SIGMA(N)
=N(N+1)(2N+1)/6 +N(N+1)/2...I HOPE YOU ARE TAUGHT THESE FORMULAE..IF NOT PLEASE COME BACK ..I SHALL GIVE ANOTHER WAY TO GO ABOUT THIS PROBLEM..
={N(N+1)/2}{(2N+1)/3 + 1}
={N(N+1)/2}{(2N+1+3)/3 }
=={N(N+1)/2}{2(N+2)/3}
=N(N+1)(N+2)/3
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