Part 5/5:
| ( \cos x ) | ( \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} ) | ( R = \infty ) |
| ( \tan^{-1} x ) | ( \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{2n + 1} ) | ( R = 1 ) |
| ( \ln(1 + x) ) | ( \sum_{n=1}^{\infty} \frac{(-1)^{n-1} x^n}{n} ) | ( R = 1 ) |
These various functions demonstrate the versatility and utility of the McLaren series in approximating functions near zero while providing insight into their behavior across specified intervals of convergence.