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

$$5\cdot \underset{50}{\underbrace{555...5}}$$$$\mathrm{find}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{digits}\mathrm{of}\mathrm{the}$$$$\mathrm{product}.$$

Answered by aleks041103 last updated on 09/Dec/23

$$5.5=25$$$$5.55=5.50+5.5=250+25=275$$$$5.555=5.500+5.55=2500+275=2775$$$$...$$$$5.555...5=277...775$$$$inthiscase$$$$5\cdot \underset{50}{\underbrace{555...5}}=2\underset{49}{\underbrace{7...7}}5$$$$\Rightarrow sumofdigitsis7.50=350$$

Commented by hardmath last updated on 09/Dec/23

$$\mathrm{cool}\mathrm{dear}\mathrm{professor}\mathrm{thankyou}$$

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

$$5\times \underset{ntimes}{555...5}$$$$=25\times \underset{ntimes}{111...1}$$$$=25$$$$25$$$$25$$$$...$$$$\underset{―}{25}$$$$=2\underset{(n-1)times}{777...75}$$$$sumofdigits=2+7(n-1)+5=7n$$$$withn=50wehave7\times 50=350✓$$

Commented by hardmath last updated on 09/Dec/23

$$\mathrm{cool}\mathrm{dear}\mathrm{professor}\mathrm{thankyou}$$

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