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 = [tex]\frac{\frac{1}{6} }{\frac{1}{6}}=1[/tex]
So series may converge or diverge.
B. common ratio = [tex]\frac{\frac{2}{6}}{\frac{1}{6}}=2[/tex]
Therefore, r > 1 series will diverge.
C. common ratio = [tex]\frac{12}{6}=2[/tex]
So r > 1, series will diverge.
D. common ratio = [tex]\frac{2}{6}=\frac{1}{3}[/tex]
r < 1 therefore, series will converge.
Option D. is the correct option.
