Byju's Answer
Standard X
Mathematics
General Form of an AP
If 1-1/3+1/5-...
Question
If
1
−
1
3
+
1
5
−
1
7
+
1
9
+
…
=
π
4
,
then the value of
1
1
×
3
+
1
5
×
7
+
1
9
×
11
+
…
is
A
π
8
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B
π
6
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C
π
4
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D
π
36
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Solution
The correct option is
D
π
8
We have,
π
4
=
(
1
−
1
3
)
+
(
1
5
−
1
7
)
+
(
1
9
−
1
11
)
+
…
…
=
2
1
×
3
+
2
5
×
7
+
2
9
×
11
+
…
⇒
1
1
×
3
+
1
5
×
7
+
1
9
×
11
+
…
=
π
8
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0
Similar questions
Q.
If
1
−
1
3
+
1
5
−
1
7
+
1
9
−
1
11
+
.
.
.
=
π
4
, then value of
1
1.3
+
1
5.7
+
1
9.11
+
.
.
.
=
Q.
Find the value of
(i) 1 + 3 + 5 = _____
(ii) 1 + 3 + 5 + 7 + 9 +11 = ________
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 =_____
Q.
Let
A
=
{
1
,
3
,
4
,
7
,
11
}
,
B
=
{
1
,
1
,
2
,
5
,
7
,
9
}
and
f
:
A
→
B
be given by
f
=
{
(
1
,
1
)
,
(
3
,
2
)
,
(
4
,
1
)
,
(
7
,
5
)
,
(
11
,
9
)
}
. Then
f
is
Q.
If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.
B = {2, 4}
A = {0}
C = {1, 9, 5, 13}
D = {5, 11, 1}
E = {13, 7, 9, 11, 5, 3, 1}
F = {2, 3, 4, 5}
Q.
If
1
1
!
9
!
+
1
3
!
7
!
+
1
5
!
5
!
+
1
7
!
3
!
+
1
9
!
1
!
=
2
n
10
!
Then n
=
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