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Sequences and Series question

2023 · Shift 1 · Q27

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PYQ Library
JEE Advanced
Mathematics
Sequences and Series
2023 · Shift 1 · Q27

Sequences and Series question

2023 · Shift 1 · Q27

JEE AdvancedMathematicsSequences and SeriesNumerical+4 / −1

Let

7 \overbrace{5 \cdots 5}^r 7

denote the

(r+2)

digit number where the first and the last digits are 7 and the remaining

r

digits are 5 . Consider the sum

S=77+757+7557+\cdots+7 \overbrace{5 \cdots 5}^{98}7

. If

S=\frac{7 \overbrace{5 \cdots 5}^{99}7+m}{n}

, where

m

and

n

are natural numbers less than 3000 , then the value of

m+n

is

Numerical answer

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