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 for n ≥ 3. t_n = \left(\frac{n-3}...

CAT Hard Sequence & Series (AP, GP, HP) MCQ

Question

Consider the sequence

t_1 = 1

t_2 = -1

, and

t_n = \left(\frac{n-3}{n-1}\right) t_{n-2} \quad \text{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:

1024144

-1024144

1012

-1012

recursive sequencessummationproblem solvingcat 2024

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