asimath
Reputation
389
Top tag
Next privilege 500 Rep.
Access review queues
 Sep 26 comment How to show that $\lim_{n\to\infty}\left\{f(c+\frac{1}{n^2})+f(c+\frac{2}{n^2})+\cdots+f(c+\frac{n}{n^2})-nf(c)\right\}=\frac{1}{2} f'(c)$ +1 really liked it. But only one question that's in my mind is after seeing your answer is that how can I develop myself think that way, or it's just practice. I think your suggestion will be very helpful to me. Thanks! Sep 26 accepted How to show that $\lim_{n\to\infty}\left\{f(c+\frac{1}{n^2})+f(c+\frac{2}{n^2})+\cdots+f(c+\frac{n}{n^2})-nf(c)\right\}=\frac{1}{2} f'(c)$ Sep 26 comment How to show that $\lim_{n\to\infty}\left\{f(c+\frac{1}{n^2})+f(c+\frac{2}{n^2})+\cdots+f(c+\frac{n}{n^2})-nf(c)\right\}=\frac{1}{2} f'(c)$ :Thanks your hints helped Sep 26 asked How to show that $\lim_{n\to\infty}\left\{f(c+\frac{1}{n^2})+f(c+\frac{2}{n^2})+\cdots+f(c+\frac{n}{n^2})-nf(c)\right\}=\frac{1}{2} f'(c)$ May 2 revised subideals of an ideal previous answer was wrong Apr 22 revised subideals of an ideal added 4 characters in body Apr 22 answered subideals of an ideal Apr 16 awarded Informed Dec 18 awarded Caucus Jul 2 awarded Curious May 10 awarded Nice Question Mar 5 awarded Critic Mar 5 comment Definite Integrals involving indeterminate quantities like log 0 @5xum here it is $\frac{\infty}{\infty}$ form Mar 5 comment Definite Integrals involving indeterminate quantities like log 0 @user133241 hint: Use L-Hospital rule. Mar 5 awarded Autobiographer Jan 16 accepted Evaluate the series Jan 15 comment Evaluate the limit of the integral of the sequence of function @labbhattacharjee : so S=$\frac{1}{2}$, for that reason I have told limit is $\frac1{2}$. Thanks! Jan 15 comment Evaluate the series @DavidMitra Please give one more hint. Jan 15 asked Evaluate the series Jan 15 comment Evaluate the limit of the integral of the sequence of function @lab bhattacharjee :Is the limit equal to 1/2