计算:[1/x(x+1)]+[1/(x+1)(x+2)]+[1/(x+2)(x+3)]=[(x+3)(x+4)]+[1/(x+4)(x+5)]
利用上式计算:(1/5*6)+(1/6*7)+(1/7*8)+(1/8*9)+(1/9*10)
过程详细
參考答案:用拆项,即:
1/x(1+x) = 1/x-1/(x+1)
所以[1/x(x+1)]+[1/(x+1)(x+2)]+[1/(x+2)(x+3)]=[(x+3)(x+4)]+[1/(x+4)(x+5)] =1/x-1/(x+5)…………(当中一加一减全部约去了)
所以(1/5*6)+(1/6*7)+(1/7*8)+(1/8*9)+(1/9*10)
=1/5-1/10=0.1