计算:a(a+1)分之1+(a+1)(a+2)分之1+(a+2)(a+3)分之1+(a+3)(a+4)分之1+...+(a+2011)(a+2012)分之1.尽量详细点,谢谢啦~~~
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/08 16:58:37
![计算:a(a+1)分之1+(a+1)(a+2)分之1+(a+2)(a+3)分之1+(a+3)(a+4)分之1+...+(a+2011)(a+2012)分之1.尽量详细点,谢谢啦~~~](/uploads/image/z/978647-23-7.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9Aa%28a%2B1%29%E5%88%86%E4%B9%8B1%2B%28a%2B1%29%28a%2B2%29%E5%88%86%E4%B9%8B1%2B%28a%2B2%29%28a%2B3%29%E5%88%86%E4%B9%8B1%2B%28a%2B3%29%28a%2B4%29%E5%88%86%E4%B9%8B1%2B...%2B%28a%2B2011%29%28a%2B2012%29%E5%88%86%E4%B9%8B1.%E5%B0%BD%E9%87%8F%E8%AF%A6%E7%BB%86%E7%82%B9%2C%E8%B0%A2%E8%B0%A2%E5%95%A6%7E%7E%7E)
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计算:a(a+1)分之1+(a+1)(a+2)分之1+(a+2)(a+3)分之1+(a+3)(a+4)分之1+...+(a+2011)(a+2012)分之1.尽量详细点,谢谢啦~~~
计算:a(a+1)分之1+(a+1)(a+2)分之1+(a+2)(a+3)分之1+(a+3)(a+4)分之1+...+(a+2011)(a+2012)分之1.
尽量详细点,谢谢啦~~~
计算:a(a+1)分之1+(a+1)(a+2)分之1+(a+2)(a+3)分之1+(a+3)(a+4)分之1+...+(a+2011)(a+2012)分之1.尽量详细点,谢谢啦~~~
用裂项法:
1/[a(a+1)]=1/a-1/(a+1)
原式=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+2011)-1/(a+2012)
=1/a-1/(a+2012)
=2012/[a(a+2012)]
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