Question

The geometric series $2.8+2.1+1.575+....$ converges to:

• A. $3.73$
• B. $4.97$
• C. $6.47$
• D. $11.20$
• E. $44.80$

Answer 1

Answer: (D)

$11.20$

The geometric series $2.8+2.1+1.575+.......$

$=2.8+2.8\times \frac{3}{4}+2.8\times {\left(\frac{3}{4}\right)}^2+..................$
We get $2.8(1+\frac{3}{4}+{\left(\frac{3}{4}\right)}^2+.............)$

$=2.8\times \frac{1}{1-\frac{3}{4}}$

$=2.8\times \frac{1}{\frac{1}{4}}$

$=2.8\times 4=11.2$