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JEE Advanced 2018 Paper 1
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© examsnet.com
Question : 47
Total: 54
For each positive integer n, let
Y
n
=
1
n
(
(
n
+
1
)
(
n
+
2
)
.
.
.
.
(
n
+
n
)
)
1
n
For
x
∊
ℝ
,let
[
x
]
be the greatest integer less than or equal to x. If
lim
n
→
∞
y
n
=
L
, then the value of
[
L
]
is_________
Your Answer:
Validate
Solution:
y
n
=
{
(
1
+
1
n
)
(
1
+
2
n
)
.
.
.
.
(
1
+
n
n
)
}
1
n
y
n
=
n
∏
r
=
1
(
1
+
r
n
)
1
n
log
y
n
=
1
n
n
∑
r
=
1
ln
(
1
+
r
n
)
⇒
lim
n
→
∞
log
y
n
=
lim
x
→
∞
n
∑
r
=
1
1
n
(
1
+
r
n
)
⇒
log
L
=
1
∫
0
ln
(
1
+
x
)
d
x
⇒
log
L
=
log
4
e
⇒
L
=
4
e
⇒
[
L
]
=
1
© examsnet.com
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