Suppose is a polynomial of degree . Prove that

by induction on . Here, is the derivative of , and is to be interpreted as .

A hint I was provided was to use integration by parts.

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- Feb 5th 2010, 08:45 AMRuntyIntegral/summation proof via induction
Suppose is a polynomial of degree . Prove that

by induction on . Here, is the derivative of , and is to be interpreted as .

A hint I was provided was to use integration by parts. - Feb 5th 2010, 09:09 AMfelper
I'll let you the case . Now, we'll suposse that the proposition is true for some poyinomial of degree . We have to prove that this proposition is true for . Let be a polynomial of degree .

Integrating by parts

But the proposition is true for the polynomial of degree k, then:

And now, conclude (Wink)