Question

The sum of infinite series $\frac{1.3}{2}+\frac{3.5}{2^2}+\frac{5.7}{2^3}+\frac{7.9}{2^4}+...\infty$.

• A. $21$
• B. $22$
• C. $23$
• D. None

Answer 1

The correct option is C $23$

$S=\frac{1.3}{2}+\frac{3.5}{2^2}+\frac{5.7}{2^3}+\frac{7.9}{2^4}+....\infty \frac{S}{2}=\frac{1.3}{2^2}+\frac{3.5}{2^3}+\frac{5.7}{2^4}+....\infty S-\frac{S}{2}=\frac{3}{2}+\frac{12}{2^2}+\frac{20}{2^3}+\frac{28}{2^4}+....\infty \frac{S}{2}=\frac{3}{2}+4(\frac{3}{2^2}+\frac{5}{2^3}+\frac{7}{2^4}+....\infty )\frac{S}{2}=\frac{3}{2}+3+\frac{5}{2}+\frac{7}{2^2}+\frac{9}{2^3}+....\infty \frac{S}{4}=\frac{3}{4}+\frac{3}{2}+\frac{5}{2^2}+\frac{7}{2^3}+....\infty \frac{S}{2}-\frac{S}{4}=\frac{15}{4}+(\frac{2}{2}+\frac{2}{2^2}+\frac{2}{2^3}+....\infty )\frac{S}{4}=\frac{15}{4}+\frac{1}{1-\frac{1}{2}}S=23$