Let denote the digit number where the first and the last digits are 7 and the remaining digits are 5 . Consider the sum . If , where and are natural numbers less than 3000 , then the value of is ....

Let 7 {5 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++7 {5 57}^{98}. If S=\frac{7 {5 57}^{99}+m}{n}, where m and n are natural numbers less than 3000 , then the value of m+n is .: Sequence & Series (Mathematics)

Let

7 \overbrace{5 \ldots 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+\ldots+7 \overbrace{5 \ldots 57}^{98}

. If

S=\frac{7 \overbrace{5 \ldots 57}^{99}+m}{n}

, where

m

and

n

are natural numbers less than 3000 , then the value of

m+n

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