JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

(444 \ldots n

times 4

)+(6666 \ldots n \text { times } 6)^2=

View answer and explanation

Correct option: D

\frac{4}{9} \cdot 10^n\left(10^n-1\right)

Option D is correct. The expression

(444 \ldots n

times 4

)+(6666 \ldots n \text { times } 6)^2

simplifies to

\frac{4}{9} \cdot 10^n(10^n-1)

after converting the repeating digits to fractions and simplifying.

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