Hi, I don't see how this leap is made. equals and this is even more confusing.
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Originally Posted by craigmain Hi, I don't see how this leap is made. equals and this is even more confusing. Your problem is not Calculus, but Algebra! Its an algebraic identity . You should know this basic identity....
Hello, See here for a way to prove it : http://www.mathhelpforum.com/math-he...484-k-b-k.html As for the initial limit, you can recognize a form of the difference quotient : Just substitute , with , in what you've been given to get the above.
Originally Posted by craigmain Hi, I don't see how this leap is made. equals and this is even more confusing. It might be easier is you see some numbers for n Notice the number of terms is the second and the power on the LHS (2 and 2, 3 and 3, 4 and 4, 5 and 5 etc), and that when all the terms are the same.
Originally Posted by Moo Hello, See here for a way to prove it : http://www.mathhelpforum.com/math-he...484-k-b-k.html As for the initial limit, you can recognize a form of the difference quotient : Just substitute , with , in what you've been given to get the above. Using a geometric series to prove that - I like that!
And, finally, taking x= y in makes every term equal to and, since there are n terms, the sum is .
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