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Byju's Answer
Standard XII
Mathematics
Definite Integral as Limit of Sum
lim n →∞[1/n+...
Question
lim
n
→
∞
[
1
n
+
1
n
+
1
+
1
n
+
2
+
⋯
+
1
2
n
]
=
[Karnataka CET 1999]
A
0
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B
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C
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D
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Solution
The correct option is
D
lim
n
→
∞
[
1
n
+
1
n
+
1
+
1
n
+
2
+
⋯
+
1
2
n
]
=
lim
n
→
∞
[
1
n
+
1
n
+
1
+
1
n
+
2
+
⋯
+
1
n
+
n
]
=
1
n
lim
n
→
∞
[
1
+
1
1
+
1
n
+
1
1
+
2
n
+
⋯
+
1
1
+
n
n
]
=
1
n
lim
n
→
∞
∑
n
r
=
0
[
1
1
+
r
n
]
=
∫
1
0
1
1
+
x
d
x
=
[
l
o
g
e
(
1
+
x
)
]
1
0
=
l
o
g
e
2
−
l
o
g
e
1
=
l
o
g
e
2