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Byju's Answer
Standard XII
Mathematics
Vn Method
Let the sum o...
Question
Let the sum of series be
n
∑
r
=
1
(
1
4
r
2
−
1
)
.
be
n
k
n
+
m
.
.Find
k
+
m
?
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Solution
T
n
=
1
2
(
1
2
n
−
1
−
1
2
n
+
1
)
∴
S
n
=
∑
T
n
=
1
2
[
(
1
1
−
1
3
)
+
(
1
3
−
1
5
)
+
(
1
5
−
1
7
)
+
.
.
.
.
.
.
+
(
1
2
n
−
1
−
1
2
n
+
1
)
]
=
1
2
(
1
−
1
[
2
n
+
1
]
)
=
n
2
n
+
1
.
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