Question

If \(f(z)=\frac{1}{z^2-3z+2}\)is expanded in the region |z|<1, then

• A. \(f(z)=\frac{1}{2}+\frac{3z}{4}+\frac{7}{8}z^2+\frac{15}{16}z^3+.......\)
• B. \(f(z)=\frac{1}{2}+\frac{4}{3}z+\frac{8}{7}z^2+\frac{16}{15}z^3+.......\)
• C. \(f(z)=\frac{1}{2}+\frac{3z}{4}+\frac{7}{9}z^2+\frac{15}{19}z^3+.......\)
• D. \(f(z)=\frac{1}{2}+\frac{3z}{4}+\frac{6}{7}z^2+\frac{15}{11}z^3+.......\)

Answer 1

The Correct Option is A

The correct answer is(A): \(f(z)=\frac{1}{2}+\frac{3z}{4}+\frac{7}{8}z^2+\frac{15}{16}z^3+.......\)