SOLUTION: using the proof of induction to prove N (summation symbol)E (i+1)i(i-1)=(N/N+1))/2^2 - N(N+1)/2

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Question 1066050: using the proof of induction to prove
N
(summation symbol)E (i+1)i(i-1)=(N/N+1))/2^2 - N(N+1)/2
i=1
is valid for all integers N(>=0)
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The sum in the left side is equal to the sum of terms %28i%2A%28i%5E2-1%29%29 from i = 1 to i = N, 

which is the same as the sum of terms i%5E3+-+i from i = 1 to i = N,


which in turn is the difference  A - B, where


A = sum i%5E3 from i= 1 to i=N,     (1)

and

B = sum i from i= 1 to i=N.       (2)


Regarding the sum (1) see the lesson 

    - Mathematical induction for sequences other than arithmetic or geometric 

in this site.


Regarding the sum (2) see the lesson 

    - Mathematical induction and arithmetic progressions 

in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Method of Mathematical induction".