Question

Which geometric series converges?

StartFraction 1 Over 81 EndFraction + StartFraction 1 Over 27 EndFraction + one-ninth + one-third + ellipsis
1 + one-half + one-fourth + one-eighth + ellipsis
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 7 (negative 4) Superscript n minus 1
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts one-fifth (2) Superscript n minus 1

Answer 1

Answer: b)
`1+(1)/(2) +(1)/(4) +(1)/(8)+...`

Explanation:

Converges means it gets smaller or the ratio has an absolute value of less than 1. The bottom 2 you can see that their ratios are greater than 1, and the top one you can see that it progressively gets bigger.

So option B is correct.