Question and Answers Forum

All Questions      Topic List

Permutation and Combination Questions

Previous in All Question      Next in All Question      

Previous in Permutation and Combination      Next in Permutation and Combination      

Question Number 42494 by Tawa1 last updated on 26/Aug/18

$$\mathrm{In}\mathrm{the}\mathrm{sequence}\mathrm{of}\mathrm{numbers}1,2,11,22,111,222,...\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{digits}$$$$\mathrm{in}999\mathrm{th}\mathrm{terms}\mathrm{is}??$$

Commented by Tinku Tara last updated on 22/Apr/21

$$1\mathrm{st}\mathrm{term}1$$$$3\mathrm{rd}\mathrm{term}11$$$$5\mathrm{th}\mathrm{term}111$$$$7\mathrm{th}\mathrm{term}1111$$$$9\mathrm{th}\mathrm{term}11111$$$$(2\mathrm{n}+1)\mathrm{term}(\mathrm{n}+1)\mathrm{time}1.$$$$999=2\times 499+1$$$$999\mathrm{term}\mathrm{will}\mathrm{have}5001\mathrm{s}$$$$\mathrm{and}\mathrm{sum}\mathrm{of}\mathrm{digits}=500$$

Answered by tanmay.chaudhury50@gmail.com last updated on 28/Aug/18

$$thegivenseriesiscombinationoftwoseries$$$$seridsare(1,11,111,...)and$$$$(2,22,222,....)$$$$firstseries(1,11,111,1111...)$$$$\{({10}^0+1),({10}^1+1),({10}^2+{10}^2+1),({10}^3+{10}^2+10+1)...\}$$$$999thterm$$$${10}^{999-1}+{10}^{997}+{10}^{996}+...+1=T_{999}$$$$T_{999}=\frac{{10}^{998}(1-\frac{1}{{10}^{999}})}{1-\frac{1}{10}}=\frac{{10}^{999}(1-\frac{1}{{10}^{999}})}{9}$$$$$$$$T_{999}=\frac{{10}^{999}-1}{9}=f\left(10\right)$$$$$$$$$$

Commented by tanmay.chaudhury50@gmail.com last updated on 27/Aug/18

$$checktheanswer$$

Commented by Tawa1 last updated on 27/Aug/18

$$\mathrm{Oh},\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know}\mathrm{the}\mathrm{answer}.\mathrm{I}\mathrm{will}\mathrm{just}\mathrm{write}\mathrm{your}$$$$\mathrm{solution}\mathrm{sir}.\mathrm{is}\mathrm{the}\mathrm{answer}\mathrm{whole}\mathrm{number}\mathrm{or}\mathrm{fraction}\mathrm{if}\mathrm{you}\mathrm{solve}$$$$\mathrm{further}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com