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WBJEE 2020 Math Solved Paper
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© examsnet.com
Question : 62
Total: 75
Let 0 < α < β < 1. Then
lim
n
→
∞
n
∑
k
=
1
1
(
k
+
α
)
∫
1
(
k
+
β
)
d
x
1
+
x
is
log
e
β
α
log
1
+
β
1
+
α
log
e
1
+
α
1
+
β
∞
Validate
Solution:
lim
n
→
∞
n
∑
k
=
1
[
log
|
1
+
x
|
]
1
∕
k
+
β
1
∕
k
+
α
=
lim
n
→
∞
n
∑
k
=
1
(
log
(
1
+
1
k
+
α
)
−
log
(
1
+
1
k
+
β
)
)
=
lim
n
→
∞
n
∑
k
=
1
(
log
(
k
+
α
+
1
k
+
α
)
−
log
(
k
+
β
+
1
k
+
β
)
)
=
log
(
β
+
1
α
+
1
)
© examsnet.com
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