①当n为奇数时,
Sn=b1b2-b2b3+b3b4-b4b5+…+（-1）^(n-1)bnbn+1
=b1b2-b2b3+b3b4-b4b5+…+bnbn+1
=b1b2+b3（b4-b2）+b5（b6-b4）+…+bn（bn+1-bn-1）
=(1*5/3)+4（b3+b5+…+bn）
=5/3+4*[7/3+(2n+1)/3]*(n-1)/2/2
=5/3+(7+2n+1)(n-1)/3
=5/3+(8+2n)(n-1)/3
=5/3+(8n+2n^2-8-2n)/3
=(2n^2+6n-3)/3
②当n为偶数时,
b1b2-b2b3+b3b4-b4b5+…+（-1）^(n-1)bnbn+1
=b2（b1-b3）+b4（b3-b5）+…+bn（bn-1-bn+1）
=-4（b2+b4+…+bn）
=-4*[5/3+(2n+1)/3]*n/2/2
=-(5+2n+1)*n/3
=-(2n^2+6n)/3