Tardigrade
Tardigrade - CET NEET JEE Exam App
Exams
Login
Signup
Tardigrade
Question
Mathematics
The value of lim n arrow ∞[(1/n a)+(1/n a+1)+(1/n a+2)+⋅s+(1/n b)] is
Q. The value of
lim
n
→
∞
[
na
1
+
na
+
1
1
+
na
+
2
1
+
⋯
+
nb
1
]
is
181
154
Integrals
Report Error
A
lo
g
(
ab
)
B
lo
g
(
a
/
b
)
C
lo
g
(
b
/
a
)
D
−
lo
g
(
ab
)
Solution:
The given limit
L
=
n
→
∞
lim
[
na
1
+
na
+
1
1
+
na
+
2
1
+
⋯
+
na
+
n
(
b
−
a
)
1
]
=
n
→
∞
lim
r
=
0
∑
(
b
−
a
)
n
na
+
r
1
=
n
→
∞
lim
n
1
r
=
0
∑
(
b
−
a
)
n
a
+
r
/
n
1
=
0
∫
(
b
−
a
)
a
+
x
d
x
=
[
lo
g
(
a
+
x
)
]
0
b
−
a
=
lo
g
b
−
lo
g
a
=
lo
g
(
b
/
a
)