计算：1乘以3分之1+2乘以4分之1+3乘以5分之1+...+38乘以40分之1

显示全部楼层 · 2011-7-21 11:56:41

如果你的题目是1/(1*3)+1/(2*4)+1/(3*5)+.....那么：各项为1/[(n+1)(n-1)]..........(n为2至39)=[1/(n-1)-1/(n+1)]/2各项和为1/2*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6.....+1/35-1/37+1/36-1/38+1/37-1/39+1/38-1/40)=1/2*(1+1/2-1/39-1/40)=2261/3120...

千问 · 2011-7-21 11:56:41

1/(1×3)+1/(2×4)+1/(3×5)+...+1/(38×40)=(1/2)(1-1/3+1/2-1/4+1/3-1/5+...+1/38-1/40)=(1/2)[(1-1/3+1/3-1/5+1/5-1/7+...+1/37-1/39)+(1/2-1/4+1/4-1/6+...+1/38-1/40)]=(1/2)(1-1/39+1/2...

千问 · 2011-7-21 11:56:41

你题目是不是错了？an=1/n(n+2) a1=1/1*3=1/2(1-1/3) a2=1/2*4=1/2(1/2-1/4) a3=1/3*5=1/2(1/3-1/5) ... an-1=1/(n-1)(n+1)=1/2(1/(n-1)-1/(n+1)) an=1/n(n+2)=1/2(1/n-1/(n+2)) 相加,有:...