
裂项相消法an=1/2(1/n-1/n+2)所以sn=a1+a2+a3+~~+an =1/2(1/1-1/3+1/2-1/4+1/3-1/5+~~+1/n-1/n+2) =1/2(1/1+1/2-1/n+1-1/n+2) =3/4-2n+3/2(n+1)(n+2)几乎所有类似的数列都可用"裂项相消法"

裂项相消法an=1/2(1/n-1/n+2)所以sn=a1+a2+a3+~~+an =1/2(1/1-1/3+1/2-1/4+1/3-1/5+~~+1/n-1/n+2) =1/2(1/1+1/2-1/n+1-1/n+2) =3/4-2n+3/2(n+1)(n+2)几乎所有类似的数列都可用"裂项相消法"