निम्न श्रेणियों के n पदों का योग कीजिए |
`(1)/(2.4)+(1)/(4.6)+(1)/(6.8)+…`

Answer

`(1)/(4(1+(1)/(n)))`

Explanation

(iv) `T_(n)=1+(1)/(3)+(1)/(3^(2))+…nपदों तक=(1[1-((1)/(3))^(n)])/(1-1//3)=(3)/(2)(1-(1)/(3^(n)))`
अब `S_(n)=(3)/(2)(1+1+1…nपदों तक)-[(1)/(3)+(1)/(3^(2))+…nपदों तक]`
`=(3)/(2)(n-((1)/(3){1-((1)/(3))^(n)})/(1-(1)/(3)))=(3)/(2)[n-(1)/(2)(1-(1)/(3^(n)))]=(1)/(4)(6n-3+(1)/(3^(n-1)))`