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Joint Entrance Examination
Mathematics
Definite Integration
Question 120
Question 120 of 246
Easy
MCQ
\[\mathop {Lim}\limits_{n \to \infty } \sum\limits_{r = 1}^n {{1 \over n}{e^{{r \over n}}}} \] is
A
\[e+1\]
B
\[e-1\]
C
\[1-e\]
D
\[e\]
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Official solution
\[\mathop {Lim}\limits_{n \to \infty } \sum\limits_{r = 1}^n {{1 \over n}} {e^{{r \over n}}}\,\,\] \[\left[ {} \right.\] Using definite integrals as limit of sum \[\left. {} \right]\] \[ = \int\limits_\theta ^1 {{e^x}} dx = e - 1\]
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