已知数列an中,a1=2,an+1=an+2（n属于N*）数列bn满足bn=1/anan+1,求bn前十项和

a(n+1)=an+2a(n+1)-an =2an -a1 =2(n-1)an = 2nbn=1/[an.a(n+1)]= (1/4)( 1/n - 1/(n+1)] Sn =b1+b2+...+bn= (1/4)( 1 - 1/(n+1)] = n/[4(n+1)]S10 = 10/44 = 5/22