`1/1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+4+...+n)=200/101`

`⇒1/(1.2:2)+1/(2.3:2)+1/(3.4:2)+1/(4.5:2)+...+1/(n.(n+1):2)=200/101`

`⇒1:1.2/2+1:2.3/2+1:3.4/2+1:4.5/2+...+1:(n.(n+1))/2=200/101`

`⇒2/1.2+2/2.3+2/3.4+2/4.5+...+2/(n.(n+1))=200/101`

`⇒2.(1/1.2+1/2.3+1/3.4+1/4.5+...+1/(n.(n+1)))=200/101`

`⇒2.(1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/n-1/(n+1))=200/101`

`⇒2.(1-1/(n+1))=200/101`

`⇒1-1/(n+1)=200/101:2`

`⇒1-1/(n+1)=100/101`

`⇒1/(n+1)=1-100/101`

`⇒1/(n+1)=1/101`

`⇒n+1=101`

`⇒n=101-1`

`⇒n=100`

`Vậy` `n=100`