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Byju's Answer
Standard X
Mathematics
Sum of N Terms of an AP
n∈ N 1+1√2+1...
Question
n
∈
N
1
+
1
√
2
+
1
√
3
+
.
.
.
.
.
.
.
.
+
1
√
n
=
S
n
then
S
n
=
?
A
√
n
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B
<
√
n
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C
≤
√
n
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D
≥
√
n
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Solution
The correct option is
C
≥
√
n
s
n
=
n
2
[
a
+
l
]
s
n
=
n
2
[
1
+
1
√
n
]
s
n
=
n
2
[
1
+
√
n
√
n
]
s
n
=
n
+
√
n
2
s
n
≥
√
n
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0
Similar questions
Q.
Statement I
For every natural number
n
≥
2
1
√
1
+
1
√
2
+
⋯
+
1
√
n
>
√
n
Statement II
For every natural number
n
≥
2
√
n
(
n
+
1
)
<
n
+
1
Q.
In an AP,
t
n
denotes
n
t
h
terms and
S
n
denotes sum of
n
terms. If
t
m
=
1
n
and
t
n
=
1
m
, find
S
m
n
.
Q.
For all
n
∈
N
,
1
+
1
√
2
+
1
√
3
+
…
+
1
√
n
=
S
n
,then
S
n
is
Q.
Let
S
n
=
1
+
2
+
3
+
.
.
.
+
n
and
P
n
=
S
2
S
2
−
1
⋅
S
3
S
3
−
1
⋅
S
4
S
4
−
1
⋅
⋅
⋅
S
n
S
n
−
1
where
n
∈
N
,
(
n
≥
2
)
.
Then
lim
n
→
∞
P
n
=
Q.
Let
S
n
=
n
(
n
+
1
)
(
n
+
2
)
+
n
(
n
+
2
)
(
n
+
4
)
+
n
(
n
+
3
)
(
n
+
6
)
+
.
.
.
.
.
.
+
1
6
n
, then
lim
n
→
∞
S
n
is
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