\(a,\left(2^{2007}+2^{2006}\right):2^{2006}=2^{2007}:2^{2006}+2^{2006}:2^{2006}=2+1=3\\ b,\left(3^{2011}+3^{2010}\right):3^{2010}=3^{2011}:3^{2010}+3^{2010}:3^{2010}=3+1=4\\ c,\left(5^{2001}+5^{2000}\right):5^{2000}=5^{2001}:5^{2000}+5^{2000}:5^{2000}=5+1=6\)

Tương tự là d,e,f và kết quả đúng lần lượt là 5,7,8 nha

59/10

5h26p

24h60p

27p19 giây

59/10

5h26p

24h60p

27p19 giây

59/10

5h26p

24h60p

27p19 giây

H= giờ
p= phút

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+\(\frac{9}{10}\)=\(\frac{19}{10}\)

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

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

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

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

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

\(=1+2\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=1+2\times\frac{9}{20}\)

\(=1+\frac{9}{10}\)

\(=\frac{19}{10}\)

b)\(2S=2\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{20}}\right)\)

\(2S=1+\frac{1}{2}+...+\frac{1}{2^{19}}\)

\(2S-S=\left(1+\frac{1}{2}+...+\frac{1}{2^{19}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{20}}\right)\)

\(S=1-\frac{1}{2^{20}}\)

c)đặt A=1+2+2^2+2^3+...+2^2006+2^2007.

2A=2(1+2+2^2+2^3+...+2^2006+2^2007)

2A=2+2^2+2^3+...+2^2008

2A-A=(2+2^2+2^3+...+2^2008)-(1+2+2^2+2^3+...+2^2006+2^2007)

A=2^2008-1

\(C=\dfrac{2006\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2007}\right)}{\left(1+\dfrac{2005}{2}\right)+\left(1+\dfrac{2004}{3}\right)+...+\left(1+\dfrac{1}{2006}\right)+1}\)

\(=\dfrac{2006\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2007}\right)}{\dfrac{2007}{2}+\dfrac{2007}{3}+...+\dfrac{2007}{2007}}=\dfrac{2006}{2007}\)

\(a_{n-1}=\frac{1}{1+2+3+...+n}=\frac{2}{n\left(n+1\right)}\)=>\(1-a_{n-1}=1-\frac{2}{n\left(n+1\right)}=\frac{n\left(n+1\right)-2}{n\left(n+1\right)}=\frac{\left(n-1\right)\left(n+2\right)}{n\left(n+1\right)}\)

\(A=\left(1-\frac{2}{2.3}\right)\left(1-\frac{2}{3.4}\right)........\left(1-\frac{2}{2006.2007}\right)\)

\(=\left(\frac{1.4}{2.3}\right)\left(\frac{2.5}{3.4}\right)\left(\frac{3.6}{4.5}\right)........\left(\frac{2005.2008}{2006.2007}\right)\)\(=\frac{\left(1.2.3......2005\right)\left(4.5.6.....2008\right)}{\left(2.3.4.....2006\right)\left(3.4.5....2007\right)}=\frac{1.2008}{2006.3}=\frac{1004}{3009}\)