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$\lim\limits_{n\to \infty}\sum\limits_{r=1}^n\large\frac{\pi}{n}$$\sin\large\frac{\pi r}{n}$ is

$(a)\;1\qquad(b)\;2\qquad(c)\;3\qquad(d)\;4$

1 Answer

Given limit=$\pi\int_0^1\sin(\pi x)dx$
$\qquad\qquad=-\big[\cos \pi x\big]_0^1$
$\qquad\qquad=1$
Hence (a) is the correct answer.
answered Dec 24, 2013 by sreemathi.v
 

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