l i m π → ∞ ∑ n r = 1 1 n e r n i s [AIEEE 2004] Options: A . &nbspe + 1 B . &nbspe - 1 C . &nbsp1 - e D . &nbspe

Answer: Option B : B l i m π → ∞ ∑ n r = 1 1 n e r n = ∫ 1 0 e x d x = [ e x ] 1 0 = e − 1

limπ→∞∑nr=1 1nern is [AIEEE 2004]

Question

l i m_{π \to \infty} \sum_{r = 1}^{n} \frac{1}{n} e^{\frac{r}{n}} i s

[AIEEE 2004]

Options:

A . e + 1

B . e - 1

C . 1 - e

D . e

Answer: Option B
:
B

l i m_{π \to \infty} \sum_{r = 1}^{n} \frac{1}{n} e^{\frac{r}{n}} = \int_{0}^{1} e^{x} d x = [e^{x}]_{0}^{1} = e - 1

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