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limit n tends to infinity.....summation of r/(n^2+n+r)...from r=1 to r=n is???? a)0. b)1/3. c)1/2 d)1 answer is 1/2 ...howww???? plzzz


8 years ago

Jitender Singh
IIT Delhi
158 Points
							Ans:$L = \lim_{n\rightarrow \infty }\sum_{r = 1}^{n}\frac{r}{n^{2}+r+n}$$L = \lim_{n\rightarrow \infty }\frac{1}{n}\sum_{r = 1}^{n}\frac{\frac{r}{n}}{1+\frac{r}{n^{2}}+\frac{1}{n}}$$\frac{r}{n} = x$$\lim_{n\rightarrow \infty }\frac{1}{n} = dx$$L = \int_{0}^{1}x.dx = (\frac{x^{2}}{2})_{0}^{1} = \frac{1}{2}$Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

6 years ago
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