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Byju's Answer
Standard IX
Mathematics
Fractional Exponent
Find the sum ...
Question
Find the sum of
1
⋅
2
2
+
2
⋅
3
2
+
3
⋅
4
2
+
4
⋅
5
2
+
⋯
to
n
terms.
Open in App
Solution
S
=
1
⋅
2
2
+
2
⋅
3
2
+
3
⋅
4
2
+
.
.
.
+
n
(
n
+
1
)
2
S
=
∑
n
(
n
+
1
)
2
S
=
∑
n
(
n
2
+
2
n
+
1
)
S
=
∑
n
3
+
2
∑
n
2
+
∑
n
Sum of cube of
n
natural number will be
(
n
(
n
+
1
)
2
)
2
Sum of square of
n
natural number will be
(
n
(
n
+
1
)
(
2
n
+
1
)
6
)
Sum of
n
natural number will be
(
n
(
n
+
1
)
2
)
S
=
(
n
(
n
+
1
)
2
)
2
+
2
(
n
(
n
+
1
)
(
2
n
+
1
)
6
)
+
(
n
(
n
+
1
)
2
)
S
=
n
(
n
+
1
)
(
3
n
2
+
11
n
+
10
12
)
S
=
n
(
n
+
1
)
(
n
+
2
)
(
3
n
+
5
)
12
Suggest Corrections
1
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