Question

The sequence $S=i+2i^2+3i^3+\dots \dots$ upto $100$ terms simplifies to where $i=\sqrt{-1}$

• A. $50(1-i)$
• B. $25i$
• C. $25(1+i)$
• D. $100(1-i)$

Answer 1

Answer: (A)

$S=i+2i^2+3i^3+\dots +100i^{100}$
$iS=i^2+2i^3+\dots +100i^{101}$
$S(1-i)=i+i^2+i^3+\dots +i^{100}-100i^{101}$
$S=\frac{-100i}{1-i}=\frac{-100i(1+i)}{2}=-50(i-1)=50(1-i)$