Find the sum of the following AP; 1^2-2^2+3^2-4^2+....to 50 terms
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Answer:
Step-by-step explanation:
The sum is
=
(
−
1
)
n
+
1
n
(
n
+
1
)
2
Explanation:
The
n
t
h
term is
=
(
−
1
)
n
+
1
n
2
The sum is
S
=
1
2
−
2
2
+
3
2
−
4
2
+
5
2
−
6
2
+
...
...
.
.
+
(
n
−
1
)
2
−
n
2
,
∀
n
∈
N
If
n
is even
S
=
(
1
2
−
2
2
)
+
(
3
2
−
4
2
)
+
(
5
2
−
6
2
)
+
...
...
+
(
(
n
−
1
)
2
−
n
2
)
S
=
(
1
−
2
)
(
1
+
2
)
+
(
3
−
4
)
(
3
+
4
)
+
(
5
−
6
)
(
5
+
6
)
+
...
+
(
(
n
−
1
−
n
)
(
n
−
1
+
n
)
S
=
(
−
1
)
(
1
+
2
)
+
(
−
1
)
(
3
+
4
)
+
(
−
1
)
(
5
+
6
)
+
...
.
+
(
(
−
1
)
(
n
−
1
+
n
)
S
=
(
−
1
)
(
(
1
+
2
)
+
(
3
+
4
)
+
(
5
+
6
)
+
...
.
+
(
n
−
1
)
+
n
)
=
(
−
1
)
⋅
n
2
(
1
+
n
)
=
(
−
1
)
n
(
n
+
1
)
2
If
n
is odd
S
=
(
−
1
)
n
+
1
n
(
n
+
1
)
2
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