\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}+\frac{1}{21.23}\)

\(A=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}+\frac{2}{21.23}\right)\)

\(A=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}+\frac{1}{21}-\frac{1}{23}\right)\)

\(A=\frac{1}{2}\left(1-\frac{1}{23}\right)\)

\(A=\frac{1}{2}.\frac{22}{23}\)

\(A=\frac{11}{23}\)

\(\frac{1}{1.3}\)+\(\frac{1}{3\cdot5}\)+................+\(\frac{1}{19.21}\)

Đặt A = \(\frac{1}{1.3}\)+\(\frac{1}{3\cdot5}\)+.............+\(\frac{1}{19.21}\)

Nhân cả 2 vế của A với 2 ta có :

2A = \(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+............+\(\frac{2}{19.21}\)

2A = \(\frac{1}{1}\)-\(\frac{1}{3}\)+ \(\frac{1}{3}\) -  \(\frac{1}{5}\)+ ............ + \(\frac{1}{19}\)- \(\frac{1}{21}\)

2A = \(\frac{1}{1}\)- \(\frac{1}{21}\)

2A = \(\frac{20}{21}\)

  A = \(\frac{20}{21}\): 2 

  A = \(\frac{10}{21}\)

=1/1.3.5+1/3/5/7+1/5.7.9+......+1/17/19/21

=1/4.(5-1/1.3.5+7-3/3.5.7+.....+21-17/17/19/21

=1/4.(5/1.3.5-1/1.3.5+7/3.5.7-3/3.5.7+.....+21/17.19.21-17/17.19.21

=1/4.(1/1.3-1/3.5+1/3.5-1/5.7+.....+1/17.19-1/19.21)

=1/4.(1/3.1/21.17)

=1/4.3200/9603

= 800/9603

            Chúc bạn học tốt^^

Đặt \(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{17.19.21}\)

\(\Rightarrow4A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+...+\frac{4}{17.19.21}\)

\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{17.19}-\frac{1}{19.21}\)

\(=\frac{1}{1.3}-\frac{1}{19.21}=\frac{44}{133}\)

\(\Rightarrow A=\frac{44}{133}\div4=\frac{11}{133}\)

ai trả lời hộ mình đi

A.-9/2

b.-5/7

C.5/287

D.302/105

nêu cách tính nha bạn 

kho the

Ta có: \(B=1\cdot3+3\cdot5+\cdots+19\cdot21\)

\(=1\left(1+2\right)+3\left(3+2\right)+\cdots+19\left(19+2\right)\)

\(=\left(1^2+3^2+\cdots+19^2\right)+2\left(1+3+\cdots+19\right)\)

Đặt \(A=1^2+3^2+\cdots+19^2\)

\(=1^2+2^2+\cdots+20^2-\left(2^2+4^2+\cdots+20^2\right)\)

\(=\left(1^2+2^2+\cdots+20^2\right)-2^2\left(1^2+2^2+\cdots+10^2\right)\)

\(=\frac{20\left(20+1\right)\left(2\cdot20+1\right)}{6}-4\cdot\frac{10\left(10+1\right)\left(2\cdot10+1\right)}{6}\)

\(=\frac{20\cdot21\cdot41}{6}-4\cdot\frac{10\cdot11\cdot21}{6}=10\cdot7\cdot41-4\cdot5\cdot11\cdot7\)

=2870-1540

=1330

Đặt C=1+3+...+19

Số số hạng của dãy số là: \(\frac{19-1}{2}+1=\frac{18}{2}+1=9+1=10\) (số)

Tổng của dãy số là: \(\left(19+1\right)\cdot\frac{10}{2}=20\cdot\frac{10}{2}=10\cdot10=100\)

Ta có: B\(=\left(1^2+3^2+\cdots+19^2\right)+2\left(1+3+\cdots+19\right)\)

=1330+2*100

=1330+200

=1530