Bài 1:`K=4/2.4 +4/4.6 +....+4/2008.2010`
⇒`K=2/1.2+2/2.3+.....+2/1004.1005`
⇒`K=2.(1/1.2+...+1/1004.1005)`
⇒`K=2.(1-1/2+1/2-1/3+1/3-....+1/1004-1/1005)`
⇒`K=2.(1-1/1005)`
⇒`K=2.(1004/1005)`
⇒`K=2008/1005`
Bài 2:Ta có:
`1/13+1/14+1/15< 1/13+1/13+1/13=3/13`
`1/61+1/62+1/63<1/61+1/61+1/61=3/61`
⇒`S<1/5+3/13+3/61`
⇒`S<1163/3965<1/2`
⇒`Đpcm`