Let S=109+108/5+107/(5²)+.+2/(5¹⁰⁷)+1/(5¹⁰⁸). Then the value of (16 S-(25)⁻⁵⁴) is equal to _ _ _ _ _ _.

Sequence and Series: JEE Main 2023 Mathematics question

JEE Main 2023 · 11 Apr, Morning shift · Q46

JEE Main 202311 Apr, Morning shiftMathematicsMediumSequence and Series179× since 2002

Let

S=109+\frac{108}{5}+\frac{107}{5^{2}}+\ldots .+\frac{2}{5^{107}}+\frac{1}{5^{108}}

. Then the value of

\left(16 S-(25)^{-54}\right)

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2023 · 11 Apr, Morning shift · Q46

JEE Main 202311 Apr, Morning shiftMathematicsMediumSequence and Series179× since 2002

Let

S=109+\frac{108}{5}+\frac{107}{5^{2}}+\ldots .+\frac{2}{5^{107}}+\frac{1}{5^{108}}

. Then the value of

\left(16 S-(25)^{-54}\right)

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.