數學問題一條

設公比為r
a2=a1*r
a3=a1*r^2
...
a6=a1*r^5
a1+a2+...+a6=1
a1(1+r+r^2+...+r^5)=1
a1[(1-r^6)/(1-r)]=1...(1)
1/a1+1/a2+...+1/a6=1 0
1/a1+1/(a1*r)+...+1/(a1*r^5)=10
1/a1[1+1/r+1/r^2+...+1/r^5)=10
1/a1{[1-(1/r)^6]/(1-1/r)}=10
[1-(1/r)^6]/(1-1/r)=10a1
from (1)
[1-(1/r)^6]/(1-1/r)=10/[(1-r^6)/(1-r)]
r[1-(1/r)^6]/(r-1)=10(1-r)/(1-r^6)
r[1-(1/r)^6](1-r^6)=10(1-r)(r-1)
r(r^6-1)(1-r^6)=10r^6(1-r)(r-1)
r(r^6-1)(r^6-1)=10r^6(r-1)(r-1)
r(r^6-1)^2=10r^6(r-1)^2
(r^6-1)^2=10r^5(r-1)^2
(1-r^6)^2=10r^5(1-r)^2
[(1-r^6)/(1-r)]^2=10r^5
a1*a2*...*a6
=a1(a1*r)...(a1*r^5)
=a1^6*r^15
=[1/(1-r^6)/(1-r)]^6*r^15
=[1/(1000r^15)]*r^15
=1/1000