Question

Which geometric series converges?

Answer 1

Answer:

Option D.

Step-by-step explanation:

For convergence or divergence of any series we should always remember

If common ratio of the terms of the geometric series r > 1 then series Diverges, for r < 1 series converges and for r = 1 series may converge or may diverge.

Now we take each series given in the figure attached

A. common ratio = $\frac{\frac{1}{6} }{\frac{1}{6}}=1$

So series may converge or diverge.

B. common ratio = $\frac{\frac{2}{6}}{\frac{1}{6}}=2$

Therefore, r > 1 series will diverge.

C. common ratio = $\frac{12}{6}=2$

So r > 1, series will diverge.

D. common ratio = $\frac{2}{6}=\frac{1}{3}$

r < 1 therefore, series will converge.

Option D. is the correct option.