Question

Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series: a1 = -1, an = \(\frac{an-1}{n}\), n ≥ 2.

Answer 1

a1 = -1, an = \(\frac{an-1}{n}\), n ≥ 2

⇒ a2 = \(\frac{a1}{2}=\frac{-1}{2}\)

a3 = \(\frac{a2}{3}=\frac{-1}{6}\)

a4 = \(\frac{a3}{4}=\frac{-1}{24}\)

a5 = \(\frac{a4}{4}=\frac{-1}{120}\)

Hence, the first five terms of the sequence are -1 , \(\frac{-1}{2},\frac{-1}{6},\frac{-1}{24},and\frac{-1}{120}\).

The corresponding series is (-1) + \((\frac{-1}{2})+(\frac{-1}{6})+(\frac{-1}{24})+(\frac{-1}{120})\) + ....