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\(3A=\frac{3}{2.3}+\frac{3}{6.3}+\frac{1}{12.3}+\frac{3}{20.3}+\frac{3}{30.3}+\frac{3}{42.3}\)
\(3A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
\(3A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{7-6}{6.7}\)
\(3A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\)
\(3A=1-\frac{1}{7}=\frac{6}{7}\Rightarrow A=\frac{2}{7}\)
em lớp 6 nha
B= 1/2 + 1/6 + 1/12 +1/20 + 1/30 + 1/42 + 1/56 + 1/72
B= 1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + 1/5*6 + 1/6*7 + 1/7*8 + 1/8*9
B=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
B=1+0-0-0-0-0-0-0-1/9
B=1-1/9
B=8/9
k em nha
Câu 2: Ta có \(S=6^2+18^2+30^2+...+126^2\)
\(S=6^2\left(1^2+3^2+5^2+...+21^2\right)\)
\(=6^2.1771=36.1771=63756\)
Hãy tích cho tui đi
vì câu này dễ mặc dù tui ko biết làm
Yên tâm khi bạn tích cho tui
Tui sẽ ko tích lại bạn đâu
THANKS
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{x\cdot\left(x+1\right)}=2\)
\(\Leftrightarrow\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{x\cdot\left(x+1\right)}=2\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{x}-\frac{1}{x+1}=2\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=2\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-2\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{-3}{2}\)
\(\Leftrightarrow\frac{-3}{-3x-3}=\frac{-3}{2}\)
\(\Leftrightarrow-3x-3=2\)
\(\Leftrightarrow-3x=2+3\)
\(\Leftrightarrow-3x=5\)
\(\Leftrightarrow x=\frac{-5}{3}\)
Vậy \(x=\frac{-5}{3}\)
3A=2.33+6.33+12.31+20.33+30.33+42.33
3A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}3A=1.21+2.31+3.41+4.51+5.61+6.71
3A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{7-6}{6.7}3A=1.22−1+2.33−2+3.44−3+...+6.77−6
3A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}3A=1−21+21−31+31−41+...+61−71
3A=1-\frac{1}{7}=\frac{6}{7}\Rightarrow A=\frac{2}{7}3A=1−71=76⇒A=72