高一数学数列

显示全部楼层 · 2009-6-11 23:20:41

1/1*2 =1/1-1/21/2*3 =1/2-1/31/3*4 =1/3-1/4......所以原式=1/1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)中间全消了，所以=1-1/(n+1)...

千问 · 2009-6-11 23:20:41

此题可用裂项法求解.1/1*2=1-1/2;1/2*3=1/2-1/3...以此类推,原试等于1-1/2+1/2-1/3...-1/n+1,最终解得答案为1-1/n+1....

千问 · 2009-6-11 23:20:41

1/n(n+1)=1/n - 1/(n+1),这是最关键的解题步骤。Sn=1/1*2+1/2*3+1/3*4+......+1/n(n+1)= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4+ …… + 1/n - 1/(n+1) = 1 - 1/(n+1) = n/(n+1)...

千问 · 2009-6-11 23:20:41

Sn=1/1*2+1/2*3+1/3*4+......+1/n(n+1)=1-1/2+1/2-1/3+1/3-1/4+......1/n-1/(n+1)=1-1/(n+1)=n/(n+1)...

千问 · 2009-6-11 23:20:41

原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.....+(1/n-1/(n+1))
=1-1/2+1/2-1/3+1/3-1/4+.....+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)...