Consider the sequence t_1=1, t_2=-1 and t_n=\left(\frac{n-3}{n-1}\right) t_{n-2} for n \geq 3. Then, the value of the sum \frac{1}{t_2}+\frac{1}{t_4}+\frac{1}{t_6}+\cdots+\frac{1}{t_{2022}}+\frac{1}{t_{2024}}, is

← CAT 2024 Slot 3 QA

CAT 2024 Slot 3 QA · Question 17

Consider the sequence $t_{1} = 1, t_{2} = - 1$ and $t_{n} = (\frac{n - 3}{n - 1}) t_{n - 2}$ for $n \geq 3$ . Then, the value of the sum $\frac{1}{t _{2}} + \frac{1}{t _{4}} + \frac{1}{t _{6}} + \dots + \frac{1}{t _{2022}} + \frac{1}{t _{2024}}$ , is

A.
-1023132
B.
-1022121
C.
-1024144
D.
-1026169

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