求1+2i+3i^2+4i^2+```+ni^(n-1)的和急求,要解题过程

Question

求1+2i+3i^2+4i^2+```+ni^(n-1)的和
急求,要解题过程

Answer 1

S=1+2i+3i^2+4i^3+```+ni^(n-1)
iS=i+2i^2+3i^3+4i^4+```+(n-1)i^(n-1)+ni^n
S-iS=1+i+i^2+...+i^(n-1)-ni^n
=(i^n-1)/(i-1)-ni^n
S=ni^n/(i-1)-(i^n-1)/(i-1)^2