24hint:infinite geometric series will be used in the soln
5 Answers
1\texttt{Let } S=\frac{1}{z}+\frac{2}{z^{2}}+... \Longrightarrow \frac{S}{z}= \frac{1}{z^{2}}+\frac{2}{z^{2}}+.... \texttt{Subtracting term by term } S\left(\frac{z-1}{z}\right)=\frac{1}{z-1} \texttt{so, } S=\frac{z}{(z-1)^{2}}
21FOOLISH DOUBT : i infite GP can th ratio R be a complex no?????? [7]
11You're right...rajat
Z=1-2i
S = 1/Z + 2/Z2 + 3/Z3 + 4/Z4 + ...........
S.Z = 1 + 2/Z + 3/Z2 + 4/Z3 + 5/Z4 + ...........
S(Z-1) = 1 + 1/Z + 1/Z2 + 1/Z3 + 1/Z4 + ...........
= Z/(Z-1)
So, S = Z/(Z-1)2 = (1-2i)/(-2i)2 = -(1-2i)/4