Thread: Series and limits review

Doing some reviewing, and here're some problems that I just seemed to not remember how to do...expediante help will be greatly appreciated

1. What is the approximation of the value of sin 1 obtained by using the fifth-degree Taylor polynomial about x=0 for sin x?

2. Do these Series converge?
Σ(1,inf) n/(n+2)
Σ(1,inf) cos(nΠ) / n

And lastly lim(x->inf) (20x^2 - 13x +5)/(5-4x^3) = 0 right? If not, how do you do it?

There's a good chance that I'll post more convergence stuff later. Can't get it into my head for some reason.

Originally Posted by Nerd

2. Do these Series converge?
Σ(1,inf) n/(n+2)

Note that,
n/(n+2) >= n/(n+n) = n/(2n) = 1/2 for sufficiently large n.
And Σ(1,inf)1/2 = +oo thus, Σ(1,inf)n/(n+2) = +oo

Σ(1,inf) cos(nΠ) / n

Note, cos(nΠ) = (-1)^{n} because it alternates between 1 and -1.
Thus, instead you can consider,
Σ(1,inf) (-1)^n/n which converges by alternating series test.