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Byju's Answer
Standard X
Mathematics
General Form of an AP
The sum of th...
Question
The sum of the first
n
terms of the series
1
+
2
+
3
+
4
+
.
.
.
.
.
.
.
+
n
is
S
n
=
n
(
n
+
1
)
2
A
True
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B
False
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Solution
The correct option is
A
True
We have,
1
+
2
+
3
+
4
+
.
.
.
.
.
.
+
n
a
=
1
,
d
=
1
We know that
S
n
=
n
2
[
2
a
+
(
n
−
1
)
d
]
Therefore,
S
n
=
n
2
[
2
×
1
+
(
n
−
1
)
×
1
]
S
n
=
n
2
[
2
+
n
−
1
]
S
n
=
n
(
n
+
1
)
2
Hence, this is the answer.
Suggest Corrections
0
Similar questions
Q.
If sum of
n
terms of a series is
S
n
=
n
(
n
+
1
)
2
, then
5
th
term is
Q.
The sum of first
n
terms of the series
1
2
1
+
1
2
+
2
2
1
+
2
+
1
2
+
2
2
+
3
2
1
+
2
+
3
+
⋯
is equal to
Q.
Find the sum to n terms of the series 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ...............................................:
Q.
Suppose a series of
n
terms is given by
S
n
=
a
1
+
a
2
+
.
.
.
+
a
n
Then
S
n
−
1
=
a
1
+
a
2
+
.
.
.
+
a
n
−
1
(
∀
n
>
1
)
and then we can write
t
n
=
S
n
−
S
n
−
1
∀
n
≥
2
for
n
=
1
we have
S
1
=
t
1
On the basis of above information answer the following questions
The sum to
n
terms of a series is
n
(
n
+
1
)
(
n
+
2
)
3
then its
n
t
h
term is given by
Q.
The sum to
n
terms of the series
(
1
×
2
×
3
)
+
(
2
×
3
×
4
)
+
(
3
×
4
×
5
)
+
…
is
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