For x>0, (1/x^2) - 1/(x+1)^2 >= 2/(x+1)^3 and therefore, for any positive integer n:
(1/n^2) - 1/(n+1)^2 >= 2/(n+1)^3
Prove this fact using the Mean Value Theorem.
Well, I suppose we should start by making f(x)=2/(x+1)^3
and so the MVT says that there is some c so that
f'(c)=f(t)-f(0)/(t-0) and then f'(c)*t+f(0)=f(t), but I don't know, I'm confused. This is how most of the other proofs in the text start off....
This is hopeless. What do you understand about this problem?
If then .
By the MVT .
Simple algebra gives us
and also .
At this point allow me to be perfectly frank.
You in the past posted questions without any evidence of effort on your part.
So at this point I must tell you that if you cannot finish this question given this extensive advice, then you must simply say to yourself “I am drowning in my own misunderstanding”.