Question

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{2005.2006}\)

\(B=\frac{a^{10}+b^{20}+c^{30}}{abc}\) với \(a=1990;b=2016\)

\(C=1^2-2^2+3^2-4^2+...+2015^2-2016^2\)

 

Answer 1

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2005}-\frac{1}{2006}\)

=> \(A=\frac{1}{1}-\frac{1}{2006}=\frac{2005}{2006}\)

Answer 2

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2005.2006}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005}-\frac{1}{2006}\)

\(A=1-\frac{1}{2006}\)

\(A=\frac{2005}{2006}\)

Answer 3

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2005.2006}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2005}-\frac{1}{2006}\)

\(\Rightarrow A=1-\frac{1}{2006}\)

\(\Rightarrow A=\frac{2005}{2006}\)

Vậy \(A=\frac{2005}{2006}\)

Answer 4

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2005}-\frac{1}{2006}\)

\(\Rightarrow A=\frac{1}{1}-\frac{1}{2006}=\frac{2005}{2006}\)

Nhớ li ke mk nha !!!

Answer 5

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2005.2006}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2005}-\frac{1}{2006}\)

\(\Rightarrow A=1-\frac{1}{2006}\)

\(\Rightarrow A=\frac{2005}{2006}\)

Answer 6

\(C=1^2-2^2+3^2-4^2+...+2015^2-2016^2\)

\(=\left(1-2\right)\left(1+2\right)+\left(3-4\right)\left(3+4\right)+...+\left(2015-2016\right)\left(2015+2016\right)\)

\(=-\left(1+2+3+4+...+2015+2016\right)\)

\(=-\frac{\left(2016+1\right).2016}{2}\)

\(=-2033136\)

Answer 7

A = \(\frac{2-1}{1.2}\) + \(\frac{3-2}{2.3}\)+ ... + \(\frac{2006-2005}{2005.2006}\)

A = \(\frac{2}{1.2}\)- \(\frac{1}{1.2}\)+ \(\frac{3}{2.3}\)- \(\frac{2}{2.3}\)+ ... + \(\frac{2006}{2005.2006}\)- \(\frac{2005}{2005.2006}\)

Rút gọn : Ta còn  

A = \(\frac{1}{1}\)- \(\frac{1}{2}\)+ \(\frac{1}{2}\)- \(\frac{1}{3}\)+ ... + \(\frac{1}{2005}\)- \(\frac{1}{2006}\)

Rút gọn: Ta còn:

\(\frac{1}{1}\)- \(\frac{1}{2006}\)= \(\frac{2005}{2006}\)