Questions tagged 'Summation of series by definite Integration'

• The value of $\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{n}{1+{{n}^{2}}}+\frac{n}{4+{{n}^{2}}}+\frac{n}{9+{{n}^{2}}}+....+\frac{1}{2n} \right]$is equal to
  Category: definite-integral | Tags: Summation of series by definite Integration
• $\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{{{1}^{3}}+{{n}^{3}}}+\frac{4}{{{2}^{3}}+{{n}^{3}}}+....+\frac{1}{2n}$is equal to
  Category: definite-integral | Tags: Summation of series by definite Integration
• $\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)-f(a)}{g(x)\,-g(a)},$
  Category: definite-integral | Tags: Summation of series by definite Integration
• $\underset{n\to \infty }{\mathop{\lim }}\,{{\left[ \frac{n!}{{{n}^{n}}} \right]}^{1/n}}$ equals
  Category: definite-integral | Tags: Summation of series by definite Integration
• $\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{n}\sum\limits_{r=1}^{2n}{\frac{r}{\sqrt{{{n}^{2}}+{{r}^{2}}}}}$ equals
  Category: definite-integral | Tags: Summation of series by definite Integration
• $\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+.....\frac{1}{2n} \right]=$
  Category: definite-integral | Tags: Summation of series by definite Integration
• $\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{k=1}^{n}{\frac{k}{{{n}^{2}}+{{k}^{2}}}}$is equals to
  Category: definite-integral | Tags: Summation of series by definite Integration
• $\underset{n\to \infty }{\mathop{\lim }}\,\,\left[ \frac{1}{n}+\frac{1}{\sqrt{{{n}^{2}}+n}}+\frac{1}{\sqrt{{{n}^{2}}+2n}}+.....+\frac{1}{\sqrt{{{n}^{2}}+(n-1)n}} \right]$ is equal to
  Category: definite-integral | Tags: Summation of series by definite Integration
• $\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{1}^{p}}+{{2}^{p}}+{{3}^{p}}+.....+{{n}^{p}}}{{{n}^{p+1}}}=$
  Category: definite-integral | Tags: Summation of series by definite Integration
• $\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{\frac{1}{n}{{e}^{\frac{r}{n}}}}$is
  Category: definite-integral | Tags: Summation of series by definite Integration

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