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AlgebraSequences & SeriesInteger TypeHard

Q10.Let

75\ldots57

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+75\ldots57

where the last term has 98 digits equal to 5 between the two 7’s. If

S=\frac{75\ldots57+m}{n},

where the numerator number has 99 digits equal to 5 between the two 7’s, and where

m

and

n

are natural numbers less than 3000, then the value of

m+n

is _.

Subjective / proof problem — work it out in the Scratchpad, then reveal the solution.

citeJEE (Advanced) 2023 — Mathematics — Paper 1

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