等比数列中,前100项和是0.1,前200项和是1.0、求前1000项和

Question

等比数列中,前100项和是0.1,前200项和是1.0、求前1000项和

Answer 1

a1(1-q^100)/(1-q)=0.1,a1(1-q^200)/(1-q)=1.0.所以1-q^100/1-q^200=0.1.假设q^100=p,则(1-p)/(1-p²)=1/(1+p)=0.1.所以p=9.所以(1-q^100)/(1-q^1000)=(1-9)/(1-9^10)=1/435848050.所以a1(1-q^1000)/(1-q)=43584805.