Chung to rang:1+1/2 mu2+1/3 mu2+1/4 mu2+....+1/100 mu2 be hon 2
đặt A=1+1/2 mu2+1/3 mu2+1/4 mu2+....+1/100 mu2
đặt B=1/2.3+1/3.4+...+1/99.100
=1/1.2+1/2.3+1/3.4+...+1/99.100
=1-1/2+1/2-1/3+...+1/99-1/100
=1-1/100<1 (1)
Mà 1<2(2)
A =1/1+1/2.2+1/3.3+...+1/100.100<1-1/2+1/2-1/3+...+1/99-1/100 (3)
từ (1),(2),(3) =>A<2
ủng hộ nhé
Rút gọn biểu thức sau
(2x-1).(1+2x)-3.(x-3)mu2 -(2+x)mu2
(2x-3)mu2 + (3-x)mu2 + 2.(3-x). (2x-3)=5
(X+5) . (5-x) +(2x-1)mu2 - (3x-1) . (X+2)-7=0
\(\left(2x-1\right)\left(1+2x\right)-3\left(x-3\right)^2-\left(2+x\right)^2\)
\(=\left(2x-1\right)\left(2x+1\right)-3\left(x^2-6x+9\right)-\left(4+4x+x^2\right)\)
\(=4x^2-1-3x^2+18x-27-4-4x-x^2\)
\(=14x-32\)
Phần b ,c giải phương trình??
\(\left(2x-3\right)^2+\left(3-x\right)^2+2\left(3-x\right)\left(2x-3\right)=5\)
\(\Leftrightarrow\left(2x-3\right)\left(2x-3+2\left(3-x\right)\right)+\left(3-x\right)^2=5\)
\(\Leftrightarrow\left(2x-3\right)\left(2x-3+6-2x\right)+\left(3-x\right)^2=5\)
\(\Leftrightarrow3\left(2x-3\right)+9-6x+x^2=5\)
\(\Leftrightarrow6x-9+9-6x+x^2=5\)
\(\Leftrightarrow x^2=5\)
\(\Leftrightarrow x=\pm\sqrt{5}\)
\(\left(x+5\right)\left(5-x\right)+\left(2x-1\right)^2-\left(3x-1\right)\left(x+2\right)-7=0\)
\(\Leftrightarrow\left(5-x\right)\left(5-x\right)+4x^2-4x+1-\left(3x^2+6x-x-2\right)-7=0\)
\(\Leftrightarrow25-x^2+4x^2-4x+1-3x^2-6x+x+2-7=0\)
\(\Leftrightarrow21-9x=0\)
\(\Leftrightarrow9x=21\)
\(\Leftrightarrow x=3\)
(2/3)mu 3.(-3/4)mu2.(-1)mu5
(2/5)mu2.(-5/12)mu2
đề yêu câu ftinhs hay tính nhanh Đoàn Đức Hiếu cho nhok cày GP nè
a) \(\left(\dfrac{2}{3}\right)^3.\left(\dfrac{-3}{4}^2\right).\left(-1\right)^5\)
\(=\dfrac{8}{27}.\dfrac{9}{16}.\left(-1\right)\)
\(=\dfrac{1}{6}.\left(-1\right)\)
=\(\dfrac{-1}{6}\)
b) \(\left(\dfrac{2}{5}\right)^2.\left(\dfrac{-5}{12}\right)^2\)
\(=\dfrac{4}{25}.\dfrac{25}{144}\)
\(=\dfrac{1}{36}\)
1)
a) 12:{390:[5.10 mu2-(5 mu3+7 mu2.x)]}=4
b) 3+2 mux-1=24-[4 mu2-(2 mu2-1)
c) (2x-6)mu2016=(2x-6)mu16
d) (x+1)+(x+2)+(x+3)+...+(x+30)=795
e) 2 mu x+2 mu x+4=272
Ai là người giải nhanh mình tick cho.Nhưng phải trả lời trước thứ 5 đấy nhé!
2/3x-1/2=x/6+[-2/3] mu2
Tim x
Tim x,y biet: (2+2)mu2 + 2(y-3)mu2 < 4
đố ai trả lời được ahihihihi !!!^^^^ Tèo còn giỏi hơn các bạn nha hihihihi!!!^^^^
Tèo đố ae trả lời được nha AhihihihHiHiiHHi đồ ngốc !!!!!!^^^^^^
chung minh rang 1\2 mu 2+1\3 mu 2+1\4 mu2+...+1\100 mu 2 < 1
ai lam day du dau tien minh se k cho nha
minh can gap lam
Đặt \(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\)
Ta có : \(\frac{1}{2^2}< \frac{1}{1.2}\)
\(\frac{1}{3^2}< \frac{1}{2.3}\)
\(\frac{1}{4^2}< \frac{1}{3.4}\)
...
\(\frac{1}{100^2}< \frac{1}{99.100}\)
\(\Rightarrow A< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(\Rightarrow A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow A< 1-\frac{1}{100}< 1\)
\(\Rightarrow A< 1\)
Vậy \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 1\).
cau1:1 pha n5.(-3 phan 5 - 10)+ 5x =x -2 phan 3
cau2:-3 phan 2(5 - 1 phan 6) +4 (x-1 phan 2)=1
cau1 : 1/x-5-3/x^-6x+5=5/x-1
cau2 : 2/x1-3x^2/x^3-1=x/x^+x+1
