Part BCSIR NET June 2025cauchy-hadamard-tests-the-coefficients-so-divide-by-n-factorial-first

Cauchy hadamard tests the coefficients so divide by n factorial first

Which of the following statements is true?

A.There exists an entire function f such that f⁽ $^{n}$ ⁾ $(0) = n! / n^{n}$ for all positive integers n.✓
B.There exists an entire function f such that f⁽ $^{n}$ ⁾ $(0) = n! n^{n}$ for all positive integers n.
C.There exists an entire function f such that f⁽ $^{n}$ ⁾(0) = (n − 1)! for all positive integers n.
D.There exists an entire function f such that f⁽ $^{n}$ ⁾(0) = n!n for all positive integers n.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Cauchy hadamard tests the coefficients so divide by n factorial first

More on this topic