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Byju's Answer
Standard XII
Mathematics
AM,GM,HM Inequality
Find the sum ...
Question
Find the sum upto
n
terms
1
1.2.3
+
1
2.3.4
+
1
3.4.5
+
.
.
.
.
.
Open in App
Solution
n
∑
x
=
1
1
x
(
x
+
1
)
(
x
+
2
)
=
n
∑
x
=
1
(
x
+
2
)
−
2
(
x
+
1
)
+
x
x
(
x
+
1
)
(
x
+
2
)
n
∑
x
=
1
1
x
(
x
+
1
)
−
n
∑
x
=
1
2
2
(
x
+
2
)
+
n
∑
x
=
1
1
(
x
+
1
)
(
x
+
2
)
=
n
∑
x
=
1
(
x
+
1
)
−
x
x
(
x
+
1
)
−
n
∑
x
=
1
(
x
+
2
)
−
x
x
(
x
+
2
)
+
n
∑
x
=
1
(
x
+
2
)
−
(
x
+
1
)
(
x
+
1
)
(
x
+
2
)
=
n
∑
x
=
1
1
x
−
1
x
+
1
−
n
∑
x
=
1
1
x
−
1
x
+
2
+
n
∑
x
=
1
1
x
+
1
−
1
x
+
2
=
n
∑
x
=
1
1
x
−
1
x
+
1
−
n
∑
x
=
1
[
(
1
2
−
1
x
+
1
)
+
(
1
x
+
1
−
1
x
+
2
)
]
+
n
∑
x
=
1
1
x
+
1
−
1
x
+
2
(
1
−
1
n
+
1
)
−
(
1
−
1
n
+
1
+
1
2
−
1
n
+
2
)
+
(
1
2
−
1
n
+
2
)
0
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