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SSC Pure Mathematics QUESTION #1285
Question 1
The Maclaurin series expansion uses the formula \(f(Z)=\sum_{n=0}^\infty a_n Z^n\) where \(a_n\) equals:
  • \(\dfrac{f^{(n)}(1)}{n!}\)
  • \(f^{(n)}(0)\)
  • \(\dfrac{f^{(n)}(0)}{n!}\)✔️
  • \(n!\cdot f^{(n)}(0)\)
Correct Answer Explanation
The Maclaurin series is the Taylor series centred at \(Z=0\): \(f(Z)=\sum_{n=0}^\infty\dfrac{f^{(n)}(0)}{n!}Z^n\). The coefficient of \(Z^n\) is \(a_n=\dfrac{f^{(n)}(0)}{n!}\).