Let 7overbrace5·s5^r7 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 + ·s + 7overbrace5·s5^987. If S = dfrac7overbrace5·s5^997 + mn, where m and n are natural numbers less than 3000, then the value of m + n is

Let 7overbrace5·s5^r7 denote the (r+2) digit number where… — JEE Advanced 2023 Mathematics PYQ

JEE Advanced 2023 · Paper 1 · numerical answer

Let

7\overbrace{5\cdots5}^{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\cdots5}^{98}7

. If

S = \dfrac{7\overbrace{5\cdots5}^{99}7 + m}{n}

, where

m

and

n

are natural numbers less than 3000, then the value of

m + n

Show answer

Answer: 1219

[JEE Advanced 2023 · Paper 1]

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