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Byju's Answer
Standard XII
Mathematics
Vn Method
Find the sum ...
Question
Find the sum of
n
terms of the series whose
n
t
h
term is
n
3
+
3
2
n
.
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Solution
T
n
=
n
3
+
3
2
n
Let
S
n
denotes the sum of the
n
terms of the given series, then
S
n
=
n
∑
k
=
1
T
k
=
n
∑
k
=
1
(
k
3
+
3
2
k
)
=
(
n
∑
k
=
1
k
3
)
+
3
2
(
n
∑
k
=
1
k
)
=
[
n
(
n
+
1
)
2
]
2
+
3
2
[
n
(
n
+
1
)
2
]
=
[
n
(
n
+
1
)
2
]
[
n
(
n
+
1
)
2
+
3
2
]
=
n
(
n
+
1
)
(
n
2
+
n
+
3
)
4
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