Homework SourseI have a questoin about power series operations i get confus
I have a questoin about power series operations.
i get confused when i have (-1)^n (1)^2n+2
or (-1)^n (-1)^2n+2 can someone tell me how to find the convergence when i have something like this?
i get confused when i have (-1)^n (1)^2n+2
or (-1)^n (-1)^2n+2 can someone tell me how to find the convergence when i have something like this?
Solution
So to conclude By the standard comparison test: since (1-1/n)^3 >= 1/2 for n>=2 and n\\sqrt{1+n^{-7}+2n^{-8} <= 2n we must have \\frac{(1-1/n)^{3}}{n\\sqrt{1+n^{-7}+2n^{-8}}}\\geq\\frac{1/2}{2n}=\\frac{1}{4n}\\] More simply by the limit comparison test \\frac{(1-1/n)^{3}/n\\sqrt{1+n^{-7}+2n^{-8}}}{1/n}\ ightarrow\\frac{1/n}{1/n}=1\\]
