Binomials Help :) (1 Viewer)

[JustRandomThings]

Hello I need help with part C of the question. Thanks in advance! ^^

 

[InteGrand]

View attachment 34015

Hello I need help with part C of the question. Thanks in advance! ^^

The method is as follows. We want to get rid of the terms with odd r in the sum in part b). To do this, sub. x = -1 into the function you used to obtain the part b) result (where you probably subbed x = +1 before), which will give us an alternating version of the sum in part b), with the odd r terms all coming with a minus sign and the even r terms with plus signs. The result of this sum will be 0 as we will we will have subbed x = -1 into a function containing (1+x) raised to a positive power. Then add this sum and its result to those in part b). This will give us twice the sum of the even terms we want. Halving will then give us the desired answer.