Question

The Laurent series expansion of \(f(z)=[\frac{2}{(z-1)(z-2)}]\) valid for \(|z-1|>1\)

• A. \(\frac{1}{(z-1)}+\frac{2}{(z-1)^3}+\frac{3}{(z-1)^5}+.....\)
• B. \(\frac{1}{(z-1)}+\frac{2}{(z-1)^3}+\frac{3}{(z-1)^3}+.....\)
• C. \(\frac{1}{(z-2)}+\frac{2}{(z-2)^3}+\frac{3}{(z-2)^3}+.....\)
• D. \(\frac{1}{(z-1)}+\frac{2}{(z-2)^3}+\frac{3}{(z-1)^3}+\frac{4}{(z-2)^4}+.....\)

Answer 1

The Correct Option is B

The correct option is (B): \(\frac{1}{(z-1)}+\frac{2}{(z-1)^3}+\frac{3}{(z-1)^3}+.....\)