5-555-5-50-find-the-sum-of-the-digits-of-the-product-

Question Number 201557 by hardmath last updated on 08/Dec/23

5 \cdot \underset{50}{\underset{⏟}{555 \dots 5}}

find the sum of the digits of the

product .

Answered by aleks041103 last updated on 09/Dec/23

5.5 = 25

5.55 = 5.50 + 5.5 = 250 + 25 = 275

5.555 = 5.500 + 5.55 = 2500 + 275 = 2775

\dots

5.555 \dots 5 = 277 \dots 775

i n t h i s c a s e

5 \cdot \underset{50}{\underset{⏟}{555 \dots 5}} = 2 \underset{49}{\underset{⏟}{7 \dots 7}} 5

\Rightarrow s u m o f d i g i t s i s 7.50 = 350

Commented by hardmath last updated on 09/Dec/23

cool dear professor thankyou

Answered by mr W last updated on 09/Dec/23

5 \times \underset{n t i m e s}{555 \dots 5}

= 25 \times \underset{n t i m e s}{111 \dots 1}

= 25

25

25

\dots

\underset{―}{25}

= 2 \underset{(n - 1) t i m e s}{777 \dots 75}

s u m o f d i g i t s = 2 + 7 (n - 1) + 5 = 7 n

w i t h n = 50 w e h a v e 7 \times 50 = 350 ✓

Commented by hardmath last updated on 09/Dec/23

cool dear professor thankyou