Can someone help me

let n be the number of lines
let A be the number of regions

when n=1, A=2
when n=2, A=4=2+2
when n=3, A=7=4+3
when n=4, A=11=7+4
when n=5, A=16=11+5
when n=6, A=22=16+6

so when n=k, A=2+2+3+4+...+(k-2)(k-1)+k
you may see that (A-1) is a trangular number
i.e. A=n(n+1)/2 +1

image:
http://i256.photobucket.com/albums/hh182/zilu_photo/d14fe604.jpg

圖片參考：http://i256.photobucket.com/albums/hh182/zilu_photo/d14fe604.jpg