计算1÷(9-4)+1÷(16-4)+1÷(25-4)+1÷(36-4)+1÷(49-4)+ .+ 1÷(10000-4)

1/(k^2-4)=1/(k^2-2^2)=1/[(k-2)(k+2)]=[1/(k-2)-1/(k+2)]/4
所以1÷(9-4)+1÷(16-4)+1÷(25-4)+1÷(36-4)+1÷(49-4)+ .+ 1÷(10000-4)
=(1/1-1/5)/4+(1/2-1/6)/4+(1/3-1/7)/4+(1/4-1/8)/4+(1/5-1/9)/4+(1/6-1/10)/4+……+(1/93-1/97)/4+(1/94-1/98)/4+(1/95-1/99)/4+(1/96-1/100)/4+(1/97-1/101)/4+(1/98-1/102)/4
=[(1/1-1/5+1/3-1/7+1/5-1/9+……+1/93-1/97+1/95-1/99+1/97-1/101)+(1/2-1/6+1/4-1/8+1/6-1/10+……+1/94-1/98+1/96-1/100+1/98-1/102)]/4
=[(1/1+1/3-1/99-1/101)+(1/2+1/4-1/100-1/102)]/4
=(1/1+1/2+1/3+1/4-1/99-1/100-1/101-1/102)/4
在后面就是纯算了,如果只是取几位小数的话,你还是按计算器吧
基本约等于0.5109