Evaluate 1 + i/2 + 1/4 + i/8 + 1/16 + i/32 + ... (where i is the imaginary unit). Express your answer in the form a+bi, where a and b are real.
+605 Don't be scared.
It's $1+i\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...\right)=1+i$.
+37146 Following thedude's work
= 1 + (1/4 + 1/16 .....) + i ( 1/2 + 1/8 + 1/32......)
= 1 + 1/4 / ( 1-1/4) + i ( 1/2 / (1-1/4) )
= 1 + 1/3 + i 2/3
= 1 1/3 + 2/3 i
