Thực hiện phép tính
g* A = 1/1.2+1/2.3+1/4.5+1/5.6
h* B = (1 + 1/2) . (1+1/3) . (1+ 1/4) .....(1+ 1/99)
Tìm x
4/x = -y/6 =0,5
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
c) Đặt \(A=1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\)
Ta có: \(A=1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\)
\(\Leftrightarrow3A=3\cdot\left(1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\right)\)
\(\Leftrightarrow3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-2\right)+...+99\cdot100\cdot\left(101-98\right)\)
\(\Leftrightarrow3\cdot A=1\cdot2\cdot3-1\cdot2\cdot3+2\cdot3\cdot4-2\cdot3\cdot4+...+98\cdot99\cdot100-98\cdot99\cdot100+99\cdot100\cdot101\)
\(\Leftrightarrow3\cdot A=99\cdot100\cdot101\)
\(\Leftrightarrow A=33\cdot100\cdot101=333300\)
b) Ta có: \(1+2-3-4+...+97+98-99-100\)
\(=\left(1+2-3-4\right)+\left(5+6-7-8\right)+...+\left(97+98-99-100\right)\)
\(=\left(-4\right)+\left(-4\right)+...+\left(-4\right)\)
\(=-4\cdot25=-100\)
d, `3,15+2,4=5,55`
e, \(\dfrac{5}{7}.\dfrac{2}{11}+\dfrac{5}{7}.\dfrac{9}{11}=\dfrac{5}{7}\left(\dfrac{2}{11}+\dfrac{9}{11}\right)=\dfrac{5}{7}.\dfrac{11}{11}=\dfrac{5}{7}.1=\dfrac{5}{7}\)
f, `1,25.3,6+3,6.8,75=3,6(1,25+8,75)=3,6.10=36`
\(h,\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\\ =1-\dfrac{1}{100}\\ =\dfrac{99}{100}\)
\(e\dfrac{5}{7}\times\left(\dfrac{2}{11}+\dfrac{9}{11}\right)=\dfrac{5}{7}\times1=\dfrac{5}{7}\)
\(f3.6\times\left(1.25+8.75\right)=3.6\times10=36\)
A= 1-2+3-4+4-5+...+99-100
A = ( 1 - 2 ) + ( 2 - 3 ) + ....+ ( 99 - 100 )
A = ( - 1 ) + ( - 1 ) +....+ ( - 1 )
A = ( - 1 ) . 50
A = - 50
B = 1.2 + 2.3 + 3.4 + 4.5 +...+ 99.100
Nhân cả 2 vế với 3, ta được:
3A=1.2.3+ 2.3.3+ 3.4.3+ 4.5.3+...... 99.100.3
= 1.2.3 + 2.3(4-1) + 3.4.(5-2) +...+ 99.100.(101-98)
= 1.2.3 + 2.3.4 -1.2.3 + 3.4.5-2.3.4 +...+ 99.100.101-98.99.100
= 99.100.101
=) B = (99.100.101) :3
B = 333300
Vậy B= 333300
A= 1-2+3-4+4-5+...+99-100
A = (1-2) + (3-4) + (4-5) + ... + (99-100)
A = (-1) + (-1) + (-1) + ...+ (-1)
A = (-1).50
A = 1
1) \(5-\left(1+\dfrac{1}{3}\right):\left(1-\dfrac{1}{3}\right)\)
\(=5-\dfrac{4}{3}:\dfrac{2}{3}\)
\(=5-\dfrac{4}{3}\cdot\dfrac{3}{2}\)
\(=5-\dfrac{4}{2}\)
\(=5-2\)
\(=3\)
b) \(\left(1+\dfrac{2}{3}-\dfrac{5}{4}\right)-\left(1-\dfrac{5}{4}\right)+2022-\dfrac{2}{3}\)
\(=1+\dfrac{2}{3}-\dfrac{5}{4}-1+\dfrac{5}{4}++2022-\dfrac{2}{3}\)
\(=\left(1-1\right)+\left(\dfrac{2}{3}-\dfrac{2}{3}\right)+\left(-\dfrac{5}{4}+\dfrac{5}{4}\right)+2022\)
\(=0+0+0+2022\)
\(=2022\)
2) \(0,7^2\cdot x=0,49^2\)
\(\Rightarrow x=\dfrac{0,49^2}{0,7^2}\)
\(\Rightarrow x=\left(\dfrac{0,49}{0,7}\right)^2\)
\(\Rightarrow x=\left(0,7\right)^2\)
\(\Rightarrow x=0,49\)
b) \(x:\left(-0,5\right)^3=\left(0,5\right)^2\)
\(\Rightarrow x=\left(0,5\right)^2\cdot\left(-0,5\right)^3\)
\(\Rightarrow x=\left(-0,5\right)^5\)
\(\Rightarrow x=-\dfrac{1}{32}\)
2:
a: =>x*0,49=0,49^2
=>x=0,49
b: =>x=(0,5)^2*(-1)*(0,5)^3=-(0,5)^5
\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{49\cdot50}\)
\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\)
\(A=1-\dfrac{1}{50}\)
\(A=\dfrac{49}{50}\)
a) \(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{201.203}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{201}-\frac{1}{203}\)
\(A=\left(\frac{1}{3}-\frac{1}{203}\right):2=\frac{100}{609}\)
Các ý còn lại cx tách như vật nha
CT chung này \(\frac{x}{n\left(n+x\right)}=\frac{1}{n}-\frac{1}{n+x}\)
\(A=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{201.203}\)
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{201.203}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{201}-\frac{1}{203}\)
\(2A=\frac{1}{3}-\frac{1}{203}=\frac{200}{609}\)
\(A=\frac{100}{609}\)
Tương tự với b thôi.
\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+\(\frac{1}{4.5}\)+\(\frac{1}{5.6}\)
A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
A=\(1-\frac{1}{3}+\frac{1}{4}-\frac{1}{6}\)
A=\(\frac{2}{3}+\frac{1}{12}\)
A=\(\frac{3}{4}\)
B=\(\left(1+\frac{1}{2}\right)\)\(\left(1+\frac{1}{3}\right)\)\(\left(1+\frac{1}{4}\right)\)...\(\left(1+\frac{1}{99}\right)\)
B=\(\frac{3}{2}\).\(\frac{4}{3}\).\(\frac{5}{4}\)...\(\frac{100}{99}\)
B=\(\frac{3.4.5...100}{2.3.4...99}\)
B=\(\frac{100}{2}\)
B=50
\(\frac{4}{x}\)=\(\frac{-y}{6}\)=0.5
\(\frac{4}{x}\)=\(\frac{-y}{6}\)=\(\frac{1}{5}\)
=> \(\frac{4}{x}\)=\(\frac{1}{5}\)=>\(x\)=\(\frac{4.5}{1}\)=9
\(\frac{-y}{6}\)=\(\frac{1}{5}\)=>\(-y\)=\(\frac{6.1}{5}\)=\(\frac{6}{5}\)=> \(y\)=\(\frac{-6}{5}\)
Vậy \(x\)= 9
\(y\)=\(\frac{-6}{5}\)
Đề bài chỉ bảo tính \(x\)nhưng mình tính cả \(y\)nếu có bài tìm cả \(y\)thì áp dụng nha