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Mathematics
If 1+(1-22 ⋅ 1)+(1-42 ⋅ 3)+(1-62 ⋅ 5)+ ldots ldots+(1-202 ⋅ 19) =α-220 β, then an ordered pair (α, β) is equal to :
Q. If
1
+
(
1
−
2
2
⋅
1
)
+
(
1
−
4
2
⋅
3
)
+
(
1
−
6
2
⋅
5
)
+
……
+
(
1
−
2
0
2
⋅
19
)
=
α
−
220
β
,
then an ordered pair
(
α
,
β
)
is equal to :
2410
188
JEE Main
JEE Main 2020
Sequences and Series
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A
(10,97)
0%
B
(11,103)
0%
C
(10,103)
100%
D
(11,97)
0%
Solution:
1
+
(
1
−
2
2
⋅
1
)
+
(
1
−
4
2
⋅
3
)
+
……
+
(
1
−
2
0
2
⋅
19
)
=
α
−
220
β
=
11
−
(
2
2
⋅
1
+
4
2
⋅
3
+
……
+
2
0
2
⋅
19
)
=
11
−
2
2
⋅
r
=
1
∑
10
r
2
(
2
r
−
1
)
=
11
−
4
(
2
11
0
2
−
35
×
11
)
=
11
−
220
(
103
)
⇒
α
=
11
,
β
=
103