I'm asking because it's a bit odd that I'm the only one posting. Should I hold off until the site is fixed? If that's the case, I'll stop with this question.
n=2∑∞(2n)!(n!)2x2n+1
I'm having some trouble solving this sum, particularly with the absolute value. Let me show you what I mean.
If I use the ratio test I get n→∞lim∣∣∣∣∣(2(n+1))!((n+1)!)2x2(n+1)+1(n!)2x2n+1(2n)!∣∣∣∣∣
I'll skip some simplification.
n→∞lim∣∣∣∣∣(2n+2)(2n+1)(n+1)2x2∣∣∣∣∣=∣∣∣∣∣41x2∣∣∣∣∣
The ratio test states that this converges only when ∣∣∣41x2∣∣∣<1
If I apply the absolute value rule along with the inequality, it leads to strange results.
−1<41x2<1
I don't feel this inequality is correct because x^2 can't be negative.
n=2∑∞(2n)!(n!)2x2n+1
I'm having some trouble solving this sum, particularly with the absolute value. Let me show you what I mean.
If I use the ratio test I get n→∞lim∣∣∣∣∣(2(n+1))!((n+1)!)2x2(n+1)+1(n!)2x2n+1(2n)!∣∣∣∣∣
I'll skip some simplification.
n→∞lim∣∣∣∣∣(2n+2)(2n+1)(n+1)2x2∣∣∣∣∣=∣∣∣∣∣41x2∣∣∣∣∣
The ratio test states that this converges only when ∣∣∣41x2∣∣∣<1
If I apply the absolute value rule along with the inequality, it leads to strange results.
−1<41x2<1
I don't feel this inequality is correct because x^2 can't be negative.