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Joint Entrance Examination
Mathematics
Indefinite Integrals
Question 357
Question 357 of 416
Medium
MCQ
lim
n
→
∞
∑
r
=
1
n
1
n
e
r
/
n
\displaystyle\lim_{n\to\infty} \sum_{r=1}^n \dfrac{1}{n}e^{r/n}
n
→
∞
lim
r
=
1
∑
n
n
1
e
r
/
n
is:
A
e
+
1
e+1
e
+
1
B
e
−
1
e-1
e
−
1
C
1
−
e
1-e
1
−
e
D
e
e
e
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Official solution
Using definite integrals as limit of sum:
lim
n
→
∞
∑
r
=
1
n
1
n
e
r
/
n
=
∫
0
1
e
x
d
x
=
e
−
1
\lim_{n\to\infty}\sum_{r=1}^n \dfrac1n e^{r/n} = \int_0^1 e^x\,dx = e-1
lim
n
→
∞
∑
r
=
1
n
n
1
e
r
/
n
=
∫
0
1
e
x
d
x
=
e
−
1
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