1. The problem statement, all variables and given/known data We have to determine whether [itex]\sum 1/n^2 + 4[/itex] is convergente or divergent 2. Relevant equations I'm trying to work the problem through trigonometric substitution. I was wondering if I could just determine that by the P-series test, the function 1/n^2 will always be larger than the other one, since p is greater than 1 in this case, both are convergent. 3. The attempt at a solution
welcome to pf! hi salazar888! welcome to pf! yes, always 0 < 1/(n^{2}+4) < 1/n^{2}, the latter sum converges (from the p-series test), so so must the former (from the direct comparison test)
Obviously, since the series [itex] \sum \frac{1}{n^2} [/itex] converges, the sum you wrote, [itex] 4 + \sum \frac{1}{n^2}[/itex] converges also. RGV
The series 1/n does not converge. It's the harmonic series. You read it wrong. I get what you're saying though.
I agree, but that is not what he wrote. We all know he meant sum 1/(n^2 + 4), but he wrote sum (1/n^2) + 4, which is very different according to standard math expression padding rules. Since he was using 'tex' anyway, he should have been able to enter "{n^2+4}" as the second argument of the '\frac' command. RGV
Yes it was my fault. I've only been on the forum for a couple of days. Thanks for the help guys. I will improve at typing the commands.