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The sum of the infinite series 1 5 ( 1 5 − 1 7 ) + ( 1 5 ) 2 ( ( 1 5 ) 2 − ( 1 7 ) 2 ) + ( 1 5 ) 3 ( ( 1 5 ) 3 − ( 1 7 ) 3 ) + ⋯ \frac{1}{5} \left( \f...

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

Question

The sum of the infinite series

15(15−17)+(15)2((15)2−(17)2)+(15)3((15)3−(17)3)+⋯\frac{1}{5} \left( \frac{1}{5} - \frac{1}{7} \right) + \left( \frac{1}{5} \right)^2 \left( \left( \frac{1}{5} \right)^2 - \left( \frac{1}{7} \right)^2 \right) + \left( \frac{1}{5} \right)^3 \left( \left( \frac{1}{5} \right)^3 - \left( \frac{1}{7} \right)^3 \right) + \cdots

is equal to

Options

A.

5408\frac{5}{408}

B.

7816\frac{7}{816}

C.

7408\frac{7}{408}

D.

5816\frac{5}{816}

cat 2024infinite seriesgeometric progressionsummation

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