Question

Tính:A: 1+1/3+1/6+1/10+...+1/171+1/190.

         B:   S=1/2+1/2^2+1/2^3+...+1/2^20.

         C: 1+2+2^2+2^3+...+2^2006+2^2007.

Answer 1

A= 1 +\(\frac{1}{3}\)+\(\frac{1}{6}\)+ .....+ \(\frac{1}{171}\)+\(\frac{1}{190}\)

A= 1 +2.(\(\frac{1}{6}\)+\(\frac{1}{12}\)+....+\(\frac{1}{342}\)+\(\frac{1}{380}\))

A=1+ 2.(\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+....+\(\frac{1}{18.19}\)+\(\frac{1}{19.20}\))

A=1+2.(\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+......+\(\frac{1}{18}\)-\(\frac{1}{19}\)+\(\frac{1}{19}\)-\(\frac{1}{20}\))

A=1 +2.(\(\frac{1}{2}\)-\(\frac{1}{20}\))

A=1+2.\(\frac{9}{20}\)=1+\(\frac{9}{10}\)=\(\frac{19}{10}\)

Answer 2

B=\(\frac{1}{2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{2^3}\)+....+\(\frac{1}{2^{20}}\)

2B= 1 +\(\frac{1}{2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{2^3}\)+......+\(\frac{1}{2^{21}}\)

2B-B= 1-\(\frac{1}{2^{21}}\)

B=1-\(\frac{1}{2^{21}}\)

Answer 3

C= 1 +2+ \(2^2\)+\(2^3\)+.......+\(2^{2007}\)

2C=2 + \(2^2\)+\(2^3\)+.....+\(2^{2007}\)+ \(2^{2008}\)

2C-C= \(2^{2008}\)-1

C=\(2^{2008}\)-1