Question

他舅来解个数学题解方程x/x(x+2)+x/(x+2)(x+4)……x/(x+8)(x+10)=1

Answer 1

2/[(n)(n+2)]=[1/n-1/(n+2)]

x/x(x+2)+x/(x+2)(x+4)……x/(x+8)(x+10)

=(x/2)[2/x(x+2)+2/(x+2)(x+4)……+2/(x+8)(x+10)]

=(x/2)[1/x-1/(x+2)+1/(x+2)-1/(x+4)……+1/(x+8)-1/(x+10)]

=(x/2)[1/x-1/(x+10)]

x=-5

经过验证

分母没有x+5

所以答案为x=-5