Telescoping series (video) | Series | Khan Academy

Video transcriptSo what we're goingto attempt to do is evaluate thissum right over here, evaluate what thisseries is, negative 2 over n plus 1 times n plus2, starting at n equals 2, all the way to infinity. And if we wanted to see whatthis looks like, it starts at n equals 2. So when n equals 2, thisis negative 2 over 2 plus 1, which is 3, times2 plus 2, which is 4. Then when n is equal to 3,this is negative 2 over 3 plus 1, which is 4, times3 plus 2, which is 5. And it just keeps goinglike that, negative 2 over 5 times 6. And it just keepsgoing on and on and on. And now, it looks pretty clearthat each successive term is getting smaller. And it's gettingsmaller reasonably fast. So it's reasonable to assumethat even though you have an infinite numberof terms, it actually might give you a finite value. But it doesn't jump outat me, at least the way that I've lookedat it right now, as to what this sumwould be, or how to actually figure out that sum. So what I want you to donow is pause th...