$1 + \frac{4}{5} + \frac{7}{{{5^2}}} + \frac{{10}}{{{5^3}}} + \ldots {\rm{to}}\;\infty $ is

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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1 + \frac{4}{5} + \frac{7}{{{5^2}}} + \frac{{10}}{{{5^3}}} + \ldots \mathrm{to}\;\infty

View answer and explanation

Correct option: C

\frac{{35}}{{16}}

Option C (

\frac{{35}}{{16}}

) is correct because it is the sum to infinity of the given arithmetico-geometric progression, calculated using the formula

{S_\infty } = \frac{a}{{1 - r}} + \frac{{dr}}{{{{\left( {1 - r} \right)}^2}}}

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\frac{3}{4}