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Question 69 - Algebra Practice | Prasnya
Q69
00:00
24 Nov 2024
Q69.
Consider the sequence
t
1
=
1
t_1 = 1
t
1
=
1
,
t
2
=
−
1
t_2 = -1
t
2
=
−
1
and
t
n
=
(
n
−
3
n
−
1
)
t
n
−
2
t_n = \left(\dfrac{n-3}{n-1}\right)t_{n-2}
t
n
=
(
n
−
1
n
−
3
)
t
n
−
2
for
n
≥
3
n \ge 3
n
≥
3
. Then, the value of the sum
1
t
2
+
1
t
4
+
1
t
6
+
…
+
1
t
2022
+
1
t
2024
\dfrac{1}{t_2} + \dfrac{1}{t_4} + \dfrac{1}{t_6} + \ldots + \dfrac{1}{t_{2022}} + \dfrac{1}{t_{2024}}
t
2
1
+
t
4
1
+
t
6
1
+
…
+
t
2022
1
+
t
2024
1
, is
A
−
1022121
-1022121
−
1022121
B
−
1026169
-1026169
−
1026169
C
−
1024144
-1024144
−
1024144
D
−
1023132
-1023132
−
1023132
Save
Check
Details
Q69
00:00
24 Nov 2024
Q69.
Consider the sequence
t
1
=
1
t_1 = 1
t
1
=
1
,
t
2
=
−
1
t_2 = -1
t
2
=
−
1
and
t
n
=
(
n
−
3
n
−
1
)
t
n
−
2
t_n = \left(\dfrac{n-3}{n-1}\right)t_{n-2}
t
n
=
(
n
−
1
n
−
3
)
t
n
−
2
for
n
≥
3
n \ge 3
n
≥
3
. Then, the value of the sum
1
t
2
+
1
t
4
+
1
t
6
+
…
+
1
t
2022
+
1
t
2024
\dfrac{1}{t_2} + \dfrac{1}{t_4} + \dfrac{1}{t_6} + \ldots + \dfrac{1}{t_{2022}} + \dfrac{1}{t_{2024}}
t
2
1
+
t
4
1
+
t
6
1
+
…
+
t
2022
1
+
t
2024
1
, is
A
−
1022121
-1022121
−
1022121
B
−
1026169
-1026169
−
1026169
C
−
1024144
-1024144
−
1024144
D
−
1023132
-1023132
−
1023132
Save
Check
Details
