Question

$\underset{n\to \infty }{lim}\left|\begin{array}{c}\frac{1}{1.3}+\frac{1}{3.5}+........+tonterms\end{array}\right|$ is equal to

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $1$
• D. $2$

Answer 1

Answer: (B)

$\frac{1}{2}$

$\underset{n\to \infty }{lim}\left(\begin{array}{c}\frac{1}{1.3}+\frac{1}{3.5}+........+tonterms\end{array}\right)$

$=\underset{n\to \infty }{lim}\frac{1}{2}\left(\begin{array}{c}\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2n-1}-\frac{1}{2n+1}\end{array}\right)$

$=\underset{n\to \infty }{lim}\frac{1}{2}\left(\begin{array}{c}1-\frac{1}{2n+1}\end{array}\right)=\frac{1}{2}(1-0)=\frac{1}{2}$