Byju's Answer
Standard XI
Mathematics
Standard Logarithm
If L= lim n →...
Question
If
L
=
lim
n
→
∞
(
n
+
2
)
!
+
(
n
+
1
)
!
(
n
+
2
)
!
−
(
n
+
1
)
!
then
10
L
is equal to
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Solution
L
=
lim
n
→
∞
(
n
+
2
)
⋅
(
n
+
1
)
!
+
(
n
+
1
)
!
(
n
+
2
)
⋅
(
n
+
1
)
!
−
(
n
+
1
)
!
=
lim
n
→
∞
(
n
+
2
)
+
1
(
n
+
2
)
−
1
=
lim
n
→
∞
n
+
3
n
+
1
=
1
∴
10
L
=
10
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Similar questions
Q.
The value of
L
=
lim
n
→
∞
(
(
n
+
1
)
(
n
+
2
)
…
.3
n
n
2
n
)
1
n
is equal to :
Q.
l
i
m
n
→
∞
(
n
+
2
)
!
+
(
n
+
1
)
!
(
n
+
2
)
!
−
(
n
+
1
)
!
is equal to
Q.
A sequence is a function whose domain is the set of natural number. A sequence
s
1
,
s
2
.
.
.
of real numbers is said to have a limit
l
if
lim
n
→
∞
s
n
=
l
. If
l
<
∞
,
then
<
s
n
>
is said to convergent. The following are well known
(i)
lim
n
→
∞
1
n
p
=
0
(
p
>
0
)
(ii)
lim
n
→
∞
x
n
=
0
(
|
x
|
<
1
)
(iii) If
lim
n
→
∞
s
n
=
l
, then
lim
n
→
∞
s
1
+
s
2
+
.
.
.
+
s
n
n
=
l
Let
f
(
x
)
=
−
1
+
|
x
−
1
|
,
g
(
x
)
=
2
−
|
x
+
1
|
then
Q.
if
S
n
=
[
1
1
+
√
n
+
1
2
+
√
n
+
.
.
.
+
1
n
+
√
n
2
]
, then
lim
n
→
∞
S
n
is equal to
Q.
lim
n
→
∞
(
n
2
−
n
+
1
n
2
−
n
−
1
)
n
(
n
−
1
)
is equal to
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