Question

B=1/4+1/16+1/64+.......+1/1024

Answer 1

\(B=\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+...+\dfrac{1}{1024}\)

\(4B=1+\dfrac{1}{4}+\dfrac{1}{16}+...+\dfrac{1}{256}\)

\(4B-B=1-\dfrac{1}{1024}\)

\(3B=\dfrac{1023}{1024}\)

\(B=\dfrac{1023}{1024}:3\)

\(B=\dfrac{341}{1024}\)

Answer 2

B=1/4+1/16+1/64+..+1/1024

B=1/4+1/4^2+1/4^3+....+1/4^5

4B=1+1/4^2+....+1/4^4

=>4B-B=1-1/4^5

=>3B=1-1/4^5

=>B=1/3-1/(4^5*3)