Question

Which of the following sequences are convergent? Select all that apply

Answer 1

r=1/5 and r=2/3 are the answers 

Answer 2

Answer:

A geometric sequence with $r=\frac{1}{5}$ and $r=\frac{2}{3}$ are convergent.

Step-by-step explanation:

Given the sequences AP and GP i.e arithmetic and geometric sequence. we have to tell the convergence of these series.

we know that the arithmetic series can never be convergent

and for Geometric series, if the common ratio r lies between |0| and |1| then the terms of GP series become smaller and smaller, approaching to → 0 in the limit and the series converges.

Hence, from the given sequence

a geometric sequence with $r=\frac{1}{5}$ and $r=\frac{2}{3}$ are convergent.