Đặt B=3+5+...+49+51

Số số hạng của dãy số là: \(\frac{51-3}{2}+1=\frac{48}{2}+1=24+1=25\) (số)

Tổng của dãy số là: \(\left(51+3\right)\cdot\frac{25}{2}=54\cdot\frac{25}{2}=25\cdot27=675\)

Đặt \(A=\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\cdots+\frac{1}{49\cdot54}\)

\(=\frac15\left(\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+\cdots+\frac{5}{49\cdot54}\right)\)

\(=\frac15\left(\frac14-\frac19+\frac19-\frac{1}{14}+\cdots+\frac{1}{49}-\frac{1}{54}\right)=\frac15\left(\frac14-\frac{1}{54}\right)\)

\(=\frac15\cdot\frac{27-2}{108}=\frac15\cdot\frac{25}{108}=\frac{5}{108}\)

Ta có: \(G=\left(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\cdots+\frac{1}{49\cdot54}\right):\frac{1-3-5-\cdots-49-51}{108}\)

\(=\frac{5}{108}:\frac{1-675}{108}=\frac{5}{-674}=\frac{-5}{674}\)

ko biết làm

đặt A = 1/4.9 + 1/9.14+ 1/14.19 + .....1/44.49

ta có 5.A = 5/4.9 + 5/9.14+ 5/14.19 + .....5/44.49 = 1/4- 1//9 + 1/9 - 1/14+........+ 1/44 -1/49 = 1/4 - 149 = 45/196

suy ra A = 9/196

đặt B = 1-3--5-...-49 = 1 - (3+5+ ....+ 49)

đặt C = 3+5+...+49        khoảng cách là d = 2

số các số hạng là (49-3)/2 + 1 = 24

tổng C = (49+3)/2 x 24 = 624

suy ra B = 1-624 = -623

vậy A = 9/196 .(-623)/89 = -9/28

-9/28

giúp tớ nhé 

tớ bị trù 690 điểm 

cảm ơn nhé 

Ta có: \(A=\left(\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+\dfrac{1}{14\cdot19}+...+\dfrac{1}{44\cdot49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)

\(\Leftrightarrow A=\dfrac{1}{5}\cdot\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+\dfrac{5}{14\cdot19}+...+\dfrac{5}{44\cdot49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)

\(\Leftrightarrow A=\dfrac{1}{5}\cdot\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{19}+...+\dfrac{1}{44}-\dfrac{1}{49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)

\(\Leftrightarrow A=\dfrac{1}{5}\cdot\left(\dfrac{1}{4}-\dfrac{1}{49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)

\(\Leftrightarrow A=\dfrac{1}{5}\cdot\left(\dfrac{49-4}{4\cdot49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)

\(\Leftrightarrow A=\dfrac{1}{5}\cdot\dfrac{45}{196}\cdot\dfrac{1-3-5-7-...-49}{89}\)

\(\Leftrightarrow A=\dfrac{9}{196}\cdot\dfrac{1-3-5-7-...-49}{89}\)

\(\Leftrightarrow A=\dfrac{9}{196}\cdot\dfrac{-623}{89}=-\dfrac{9}{28}\)

-9/28

Đặt \(A=\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right).\dfrac{1-3-5-7-...-49}{89}\)

\(=\dfrac{1}{5}\left(\dfrac{5}{4.9}+\dfrac{5}{9.14}+\dfrac{5}{14.19}+...+\dfrac{5}{44.49}\right).\dfrac{1-3-5-7-...-49}{89}\)

\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{19}+...+\dfrac{1}{44}-\dfrac{1}{49}\right).\dfrac{1-3-5-7-...-49}{89}\)

\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{49}\right).\dfrac{1-3-5-7-...-49}{89}\)

\(=\dfrac{9}{196}.\dfrac{1-3-5-7-...-49}{89}\)

Đặt \(B=1-3-5-7-..-49\)

\(=1-\left(3+5+7+...+49\right)\)

\(=1-\left\{\left(49+3\right).\left[\left(49-3\right):2+1\right]:2\right\}\)

\(=1-624\)

\(=-623\)

\(\Rightarrow\dfrac{9}{196}.\left(\dfrac{-623}{89}\right)=-\dfrac{9}{28}\)

Vậy: \(\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right).\dfrac{1-3-5-7-...-49}{89}=-\dfrac{9}{28}\)

Xét \(\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right)\)

=\(\dfrac{1}{5}\left(\dfrac{5}{4.9}+\dfrac{5}{9.14}+\dfrac{5}{14.19}+...+\dfrac{5}{44.49}\right)\)

=\(\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{19}+...+\dfrac{1}{44}-\dfrac{1}{49}\right)\)

=\(\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{49}\right)\)

=\(\dfrac{1}{5}.\dfrac{45}{196}\)

=\(\dfrac{9}{196}\)

Xét \(\dfrac{1-3-5-7-..-49}{89}\)

=\(\dfrac{1-\left(3+5+7+...+49\right)}{89}\)

CT tính sl số hạng (số cuối - số đầu ):2+1

số lượng số hạn của dãy 3+5+7+...+49 là (49-3):2+1=24

Áp dụng CT tính tổng số hạng dãy số cách đều Tổng = [ (số đầu + số cuối) x Số lượng số hạng ] : 2

=> tổng = [(3+49).24]:2=624

=>\(\dfrac{1-624}{89}\)

=\(\dfrac{-623}{89}\)

=-7

từ đó ta có \(\dfrac{9}{196}.\left(-7\right)=\dfrac{-9}{28}\)