Question

math....

1/5*9+1/9*13+1/13*17+....+1/101*105
bu hui

Answer 1

5乘9分之一
=1/4(1/5-1/9)+1/4(1/9-1/13)........
5乘9分之一+9乘13分之一+13乘17分只一........+101乘105分之一
=1/4(1/5-1/9+1/9-1/13_1/13-1/17........+1/101-1/105)
=1/4[1/5+(-1/9+1/9)+(-1/13+1/13)-1/17........+1/101-1/105]
=1/4(1/5-1/105)
=1/4*20/105
=1/21

Answer 2

1/n(n+4)=1/4*(1/n-1/(n+4))

原式=1/4[(1/5-1/9)+(1/9-1/13)+...+(1/101-1/105)]=1/4*(1/5-1/105)=1/21