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 Feb 1 comment Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ Nice solution Chris'ssister! :-) Your question and the corresponding answers provide a decent tool. :-) Feb 1 awarded Self-Learner Feb 1 revised Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ added 44 characters in body Feb 1 revised Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ deleted 201 characters in body Feb 1 comment Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ Thanks. A different solution. :-) Feb 1 revised Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ added 155 characters in body Feb 1 comment Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ Okay. No problems. :-) Generally, when people downvote, and the OP asks the reason, it is expected that the person who downvoted leave a comment about it. And hence, my assumption. Feb 1 revised Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ deleted 204 characters in body Feb 1 comment Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ Arrrrgh. Thanks. Feb 1 comment Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ @ToddWilcox Counterpoint. meta.math.stackexchange.com/q/2244/14082 Feb 1 comment Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ Added the explanation. I hope its correct. Feb 1 revised Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ added explanation for solution of differential equation. Feb 1 comment Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ A few reasons 1. It gives me oppurtunity to verify that the solution is indeed correct. (I self study, so even though I get an answer and I am pretty sure about it, there is no real way to verify the solution completely.) 2. It allows probably other people to offer me better solutions. 3. I can do so on a blog, but then it might not get the same attention on the blog. 4. MSE's editing capabilities are better than almost all other blogging software I have found. Feb 1 comment Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ Is the downvote because of self-answering? Feb 1 asked Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ Feb 1 answered Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ Jan 30 awarded Nice Answer Jan 24 awarded Civic Duty Jan 18 revised Bounds for solutions of $xe^{x} -n =0$ for $n\geq 3$ Reformatted text typed in as math for better reading. Jan 18 suggested approved edit on Bounds for solutions of $xe^{x} -n =0$ for $n\geq 3$