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(1/2*X+2/1/4)*-2/3=2/5/6
(1/2*X+9/4)*-2/3=17/6
(1/2*X+9/4)=-17/4
1/2*X=-13/2
X=-13
Câu 1 :\(P=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).....\left(1-\frac{1}{99}\right)=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{98}{100}=\frac{1}{100}\)
a: \(B=\left(-\dfrac{1}{5}-\dfrac{5}{7}+\dfrac{-3}{35}\right)+\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{2}\right)+\dfrac{1}{41}\)
\(=\dfrac{-7-25-3}{35}+\dfrac{3+2+1}{6}+\dfrac{1}{41}=\dfrac{42}{41}-1=\dfrac{1}{41}\)
Đặt \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{18.19.20}\)
\(\Rightarrow2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{18.19.20}\)
\(=\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\left(\frac{1}{18.19}-\frac{1}{19.20}\right)\)
\(=\frac{1}{2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{18.19}-\frac{1}{19.20}\)
\(=\frac{1}{2}-\frac{1}{19.20}<\)\(\frac{1}{2}\)
\(2A<\)\(\frac{1}{2}\)
\(\Rightarrow A<\)\(\frac{1}{4}\)
Vậy \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{18.19.20}<\)\(\frac{1}{4}\)
d) 7/18 . x - 2/3 = 5/18
7/18 . x = 5/18+2/3
= 17/18 : 7/18
= 17/7
e) 4/9 - 7/8 . x = -2/3
7/8 . x = 4/9 - -2/3
= 10/9 : 7/8
= 80/63
f) 1/6 + -5/7 : x = -7/18
-5/7 : x = -7/18 - 1/6
-5/7 : x = -5/9
= -5/7 : -5/9
= 9/7
Sau đó bạn thử lại kết quả nha!
Thay a,b,c lần lượt vào biểu thức...
Tính được kết quả:
a) A= \(-\frac{7}{10}\)
b) B= \(-\frac{2}{7}\)
c) C= 0
a)
\(\frac{1}{x^2+x+1}dx=\frac{1}{\left(x-\frac{1}{4}\right)^2+\left(\frac{\sqrt{3}}{2}\right)^2}dx\)
Đặt
\(\left(x-\frac{1}{4}\right)=\frac{\sqrt{3}}{2}tant\) => dx=\(\frac{\sqrt{3}}{2}\left(1+tan^2t\right)dt\) =>\(\frac{1}{x^2+x+1}dx=\frac{1}{\frac{3}{4}\left(1+tan^2t\right)+\frac{3}{4}}\left(1+tan^2t\right)dt=\frac{3}{4}dt=\frac{3}{4}t+C\)
Với \(\left(x-\frac{1}{4}\right)=\frac{\sqrt{3}}{2}tant=>t=\left(\frac{2\sqrt{3}}{4x-1}\right)\)
Câu b nhá :
\(\frac{1}{x^2+2x+2}dx=\frac{1}{\left(x+1\right)^2+\left(\sqrt{2^2}\right)}dx\)
Đặt
\(x+1=\sqrt{2}tant=>dx=\sqrt{2}\left(1+tan^2t\right)dt\)
=> \(\frac{1}{x^2+2x+3}dx=\frac{1}{2\left(tan^2t+1\right)}.\left(1+tan^2t\right)dt=\frac{1}{2}dt=\frac{1}{2}t+C\)
Với
\(x+1=\sqrt{2}tant=>tant=\frac{x+1}{\sqrt{2}}<=>t=arctan\left(\frac{x+1}{\sqrt{2}}\right)\)
a) \(\frac{1}{n}\) - \(\frac{1}{n+1}\) = \(\frac{n+1}{n\left(n+1\right)}\) - \(\frac{n}{n\left(n+1\right)}\) = \(\frac{1}{n\left(n+1\right)}\) = \(\frac{1}{n}\) . \(\frac{1}{n+1}\) =>đpcm
b) A= \(\frac{1}{2}\) - \(\frac{1}{3}\) + \(\frac{1}{3}\) - \(\frac{1}{4}\)+...+\(\frac{1}{8}\) - \(\frac{1}{9}\) +\(\frac{1}{9}\)
= \(\frac{1}{2}\) + \(\frac{1}{9}\)= \(\frac{11}{18}\)
sai rồi -7/12+8/12=1/12 mà
5/6-X=1/12
X=5/6-1/12
X=3/4
thank