1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*20101/n(n+1)【*=乘以 /=分之】两分钟够了吧
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 16:49:19
![1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*20101/n(n+1)【*=乘以 /=分之】两分钟够了吧](/uploads/image/z/1782715-67-5.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B1%2F4%2A5%E2%80%A6%E2%80%A6%2B1%2F2009%2A20101%2Fn%EF%BC%88n%2B1%EF%BC%89%E3%80%90%2A%3D%E4%B9%98%E4%BB%A5+%2F%3D%E5%88%86%E4%B9%8B%E3%80%91%E4%B8%A4%E5%88%86%E9%92%9F%E5%A4%9F%E4%BA%86%E5%90%A7)
1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*20101/n(n+1)【*=乘以 /=分之】两分钟够了吧
1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*2010
1/n(n+1)【*=乘以 /=分之】
两分钟够了吧
1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*20101/n(n+1)【*=乘以 /=分之】两分钟够了吧
1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/2009-1/2010
=1-1/2010
=2009/2010
1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*2010
=1-1/2+1/2-1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010
=(2-1)/1*2+(3-2)/2*3+(4-3)/3*4+(5-4)/4*5……+(2010-2009)/2009*2010
=(2/1*2-1/1*2)+(3/2*3-2/2*3)+(4/3*4-3/3*4)+(5/4*5-4/4*5)……+(2010/2009*2010-2009/2009*2010)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5……+1/2009-1/2010
=1-1/2010
=2009/2010