Question

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Answer 1

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Answer 2

Answer:

OPTION A

Step-by-step explanation:

This is an arithro geometric progression.

Let S be the sum of all numbers .

S = 1 + 2/5 + 3/5² + 4/5³ + ............ n/5ⁿ ..........( 1 )

= > S/5 = 1/5 + 2/5² + ..... n/5ⁿ ............( 2 )

Subtracting them we get :

S - S/5 = 1 + 1/5 + ........... - n/5

= > 4 S/5 = 1 ( 1 - 1/5ⁿ ) / ( 1 - 1/5 ) - n/5

= > 4 S/5 = 1 ( 5ⁿ - 1 ) / 5ⁿ / 4 / 5 - n / 5

= > 4 S/5 = ( 5ⁿ⁺¹ - 4 n - 5 ) / ( 4 * 5ⁿ )

= >  S = ( 5ⁿ⁺¹ ) / ( 4 . 5ⁿ ) - ( 4 n + 5 ) / ( 4.5ⁿ )

= > S = 25/16 - ( 4 n + 5 ) / ( 16. 5ⁿ.5 )

Hence the correct option is OPTION A .