Question

（1+i)+(1+i)^2+(1+i)^3+...+(1+i)^20=

Answer 1

等比数列
所以原式=(1+i)*[1-(1+i)^20]/[1-(1+i)]

(1+i)²=1+2i-1=2i
所以原式=(1+i)*[1-(2i)^10]/(-i)
=(1+i)(1+1024)/(-i)
=-1025(1+i)*i/i²
=1025i-1025

Answer 2

1/x-1/y=(y-x)/xy=3
y-x=3xy
所以x-y=-3xy

原式=[2(x-y)-14xy]/[(x-y)-2xy]
=[2(-3xy)-14xy]/[(-3xy)-2xy]
=-20xy/(-5xy)
=4