91Ó°ÊÓ

The 3rd term of an \(\mathrm{AP}\) is 34 and the 17 th term is \(-8\). Find the sum of the first 20 terms

Find the range of values of \(x\) for which each of the following series is convergent or divergent: (a) \(1+x+\frac{x^{2}}{21}+\frac{x^{3}}{31}+\frac{x^{4}}{41}+\ldots .\) (b) \(\frac{x}{1 \times 2}+\frac{x^{2}}{2 \times 3}+\frac{x^{3}}{3 \times 4}+\frac{x^{4}}{4 \times 5} \cdots\) (c) \(\sum_{n=1}^{\infty} \frac{(n+1)}{n^{3}} x^{n}\)