सिध्द कीजिए कि-
`1+(1)/(1+2)+(1)/(1+2+3)+(1)/(1+2+3+4)+…oo=2`

Explanation

(iv)माना n वाँ पद `T_(n)`है, तब
`T_(n)=(1)/(1+2+3+....+4)=(1)/(Sigman)=(1)/((n(n+1))/(2))=(2)/(n(n+1))=2((1)/(n)-(1)/(n+1))`
अब `" "S_(n)=T_(1)+T_(2)+....T_(n)`
`=2[{1-(1)/(2)}+{(1)/(2)-(1)/(3)}+{(1)/(3)-(1)/(4)}+...+{(1)/(n)-(1)/(n+1)}]`
`=2(1-(1)/(n+1))=2)(n)/(n+1))`
इसलिये,`" "S_(oo)=underset(n to oo)lim S_(n)=underset(n to oo)lim[2{1-(1)/(n+1)}]=2(1-(1)/(oo))=2=दायाँ पक्ष`