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ta phân tích thành
\(\frac{1}{1\cdot2}\)x\(\frac{2\cdot2}{2\cdot3}\)x\(\frac{3\cdot3}{3\cdot4}\)x......x\(\frac{5\cdot5}{5\cdot6}\)x\(\frac{6\cdot6}{6\cdot7}\)
Tử nhân tử mẫu nhân mẫu ta có
1x2x2x3x3x.........x5x5x6x6
1x2x2x3x3x4x....x5x6x6x7
Rút gọn ta có
\(\frac{1}{7}\)
Vậy A=\(\frac{1}{7}\)
1.
A = (22.21.20 - 2.1.0) : 3
A = 9240 : 3
A = 3080
3.A = 3080 x 3
3.A = 9240
\(A=\frac{1\cdot2+2\cdot3+3\cdot4+...+20\cdot21}{1+2-3-4+5+6-7-8+...+197+198-199-200+201}\) (1)
đặt \(B=1\cdot2+2\cdot3+3\cdot4+...+20\cdot21\)
\(3B=1\cdot2\cdot3+2\cdot3\cdot3+3\cdot4\cdot3+...+20\cdot21\cdot3\)
\(3B=1\cdot2\cdot\left(3-0\right)+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-2\right)+...+20\cdot21\cdot\left(22-19\right)\)
\(3B=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+3\cdot4\cdot5-2\cdot3\cdot4+...+20\cdot21\cdot22-19\cdot20\cdot21\)
\(3B=20\cdot21\cdot22\)
\(B=\frac{20\cdot21\cdot22}{3}=3080\) (2)
đặt \(C=1+2-3-4+5+6-7-8+...+197+197-199-200+201\)
\(C=\left(1+2-3-4\right)+\left(5+6-7-8\right)+...+\left(197+198-199-200\right)+201\)
\(C=-4+\left(-4\right)+...+\left(-4\right)+201\) có 50 số -4
\(C=-4\cdot50+201\)
\(C=-200+201\)
\(C=1\) (3)
\(\left(1\right)\left(2\right)\left(3\right)\Rightarrow A=\frac{B}{C}=\frac{30801}{1}=3080\)
Chị dùg cách tính tổng đi
1. Tìm dãy cách đều bao nhiêu
2. Từ công thức tính tổng rồi suy ra
`Answer:`
Bài 1:
a. \(\frac{1}{2}-\left(\frac{2}{3}x-\frac{1}{3}\right)=\frac{2}{3}\)
\(\Leftrightarrow\frac{1}{2}-\frac{2}{3}x+\frac{1}{3}=\frac{2}{3}\)
\(\Leftrightarrow\frac{5}{6}-\frac{2}{3}x=\frac{2}{3}\)
\(\Leftrightarrow-\frac{2}{3}=\frac{2}{3}-\frac{5}{6}\)
\(\Leftrightarrow-\frac{2}{3}x=-\frac{1}{6}\)
\(\Leftrightarrow x=-\frac{1}{6}:-\frac{2}{3}\)
\(\Leftrightarrow x=\frac{1}{4}\)
b. \(\frac{3}{x+5}=15\%\left(ĐKXĐ:x\ne-5\right)\)
\(\Leftrightarrow\frac{3}{x+5}=\frac{3}{20}\)
\(\Leftrightarrow\frac{60}{20\left(x+5\right)}=\frac{3\left(x+5\right)}{20\left(x+5\right)}\)
\(\Leftrightarrow60x=3x+15\)
\(\Leftrightarrow-3x=-45\)
\(\Leftrightarrow x=15\)
Bài 2:
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}\)
\(=\frac{49}{50}\)
a) 3/7 + 4/9 + 4/7 + 5/9
= ( 3/7 + 4/7 ) + ( 4/9 + 5/9 )
= 7/7 + 9/9
= 1 + 1
= 2
b)1/5 + 4/10 + 9/15 + 16/20 + 25/25 + 36/30 + 49/35 + 64/40 + 81/45
= 1/5 + 2/5 + 3/5 + 4/5 + 5/5 + 6/5 + 7/5 + 8/5 + 9/5
= ( 1/5 + 9/5 ) + ( 2/5 + 8/5 ) + (7/5 + 3/5 ) + ( 4/5 + 6/5 ) + 5/5
= 2 + 2 + 2 + 2 + 1
= 2 x 4 + 1
= 8 +1
= 9
c) 1/8 + 1/12 + 3/8 + 5/12
= ( 1/8 + 3/8 ) + ( 1/12 + 5/12)
= 4/8 + 6/12
= 1/2 + 1/2
= 2/4 = 1/2
mỏi tay rồi
d; (1 - \(\dfrac{1}{2}\)) x (1 - \(\dfrac{1}{3}\)) x (1 - \(\dfrac{1}{4}\)) x ... x ( 1 - \(\dfrac{1}{100}\))
= \(\dfrac{1}{2}\) x \(\dfrac{2}{3}\) x \(\dfrac{3}{4}\) x \(\dfrac{3}{4}\) x ... x \(\dfrac{99}{100}\)
= \(\dfrac{1}{100}\)
1=300
2=3774
3=3000
4 là 1275 nhé
5 là 3080 nhé