निम्नलिखित श्रेणी के 100 पदों का योगफल ज्ञात कीजिए -
`0.3+0.33+0.333+ ……`

Explanation

`S_(100)=0.3+0.33+0.333+……100` पदों तक
`=(3)/(10)+(33)/(100)+(333)/(1000)+......100` पदों तक
`=3[(1)/(10)+(11)/(100)+(111)/(1000)+....100 "पदों तक"]`
`=(3)/(9)[(9)/(10)+(99)/(100)+(999)/(1000)+......100" पदों तक"]`
`=(1)/(3)[(1-(1)/(10))+(1-(1)/(100))+(1-(1)/(1000))+....100" पदों तक"]`
`=(1)/(3)[(1+1+1+...100 " पदों तक")-((1)/(10)+(1)/(100)+(1)/(1000)+.....100 " पदों तक")]`
`=(1)/(3)[100-((1)/(10){1-(1)/(10^(100))})/(1-(1)/(10))] " " because a=(1)/(10),r=(1)/(10)`
`=(1)/(3)[100-(1)/(9){1-(1)/(10^(100))}]`
`=(100)/(3)-(1)/(27){1-(1)/(10^(100))}`.