Question

If \( S = \sum_{n=0}^{\infty} \frac{(\log x)^{2n}}{(2n)!} \), then \( S \) is equal to

• A. \( x + x^{-1} \)
• B. \( x - x^{-1} \)
• C. \( \dfrac{1}{2}\left(x + x^{-1}\right) \)
• D. None of these

Hint:

Whenever a series contains only even powers like \( \dfrac{t^{2n}}{(2n)!} \), think of the standard expansion of \( \cosh t \).

Answer 1

The Correct Option is C