\(Q=1+\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+...+\frac{2}{50\cdot51}\)
\(Q=1+2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{50\cdot51}\right)\)
\(Q=1+2\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{50}-\frac{1}{51}\right)\)
\(Q=1+2\cdot\left(\frac{1}{2}-\frac{1}{51}\right)\)
\(Q=1+\frac{49}{51}\)
\(Q=\frac{100}{51}\)
Thu gọn biểu thức: \(A=\dfrac{2^{99}+2^{98}+...+2+1^{ }}{2^{49}+2^{48}+...+2+1^{ }}-2^{50}\)
a)Cho A= \(\dfrac{2015}{2016}+\dfrac{2016}{2017}+\dfrac{2017}{2018}+\dfrac{2018}{2019}+\dfrac{2019}{2020}+\dfrac{2021}{2015}\)
Chứng minh A>6
b)Cho C=\(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+....+\dfrac{1}{3^{2010}}\)
Chứng minh rằng C<1
Cho D=\(\dfrac{1}{1^2.2^3}+\dfrac{5}{2^2.3^3}+\dfrac{7}{3^2.4^2}+.....+\dfrac{4019}{2009^2.2010^2}\)
Chứng minh rằng D<1
mấy bạn giúp mình nha. Mình cần gấp lắm TT^TT
b1: Tính A = 1.2 + 2.3 + 3.4 +...+ n. ( n+1 )
b2: Tính D = 10 + 12 + 14 +...+ 994 + 996 + 998
Giải hộ mik nha, mai ktra rùi!!!!! Thank you
Cho \(f\left(x\right)=\left(8x^2+5x-14\right)^{49}.\left(3x^3-10^2+6x+2\right)^{50}\). Sau khi thu gọn thì tổng các hệ số f(x) là bao nhiêu?
a, A =\(-2\chi^3+3\chi^2+5\) tại \(\chi=\dfrac{1}{2}\);\(\chi^2-1=0\);\(\chi^2=3\chi\)
b, B =\(-3\chi^3\gamma^2+2\chi^2\gamma^3-2\chi\) tại \(\left|\chi\right|=2\);\(\gamma=1\)
I. Tính
1) (1+\(\dfrac{2}{3}\)-\(\dfrac{1}{4}\)). 0,8- \(\dfrac{3}{4}\))\(^2\)
2) (2\(^2\): \(\dfrac{4}{3}\)-\(\dfrac{1}{2}\)).\(\dfrac{6}{5}\)-17
3)24\(\dfrac{1}{7}\):\(\dfrac{-3}{5}\)-33\(\dfrac{1}{7}\):\(\dfrac{-3}{5}\)
1.Cho \(\dfrac{m-n}{p-q}\)=\(\dfrac{n}{q}\). Chứng minh\(\dfrac{m^2+n^2}{p^2+q^2}=\dfrac{\left(m+n\right)^2}{\left(p+q\right)^2}\)(Giả thiết các tỉ số đều có nghĩa)
2.Cho \(\dfrac{2}{a}=\dfrac{1}{b}+\dfrac{1}{c}\)(a,b,c\(\ne\)0,a\(\ne\)c). Chứng minh rằng:\(\dfrac{b}{c}=\dfrac{b-a}{a-c}\)
3.Cho b2=ac.Chứng minh:\(\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a}{c}\)
4.Cho \(\dfrac{x}{3}\)=\(\dfrac{y}{4}\) và \(\dfrac{y}{5}=\dfrac{z}{6}\). Tính \(M=\dfrac{2x+3y+4z}{3x+4y+5z}\)
So sánh : a) (-39)9 và (-18)13
b)\(\dfrac{1}{101^2}+\dfrac{1}{102^2}+\dfrac{1}{103^2}+\dfrac{1}{104^2}+\dfrac{1}{105^2}\) và \(\dfrac{1}{2^2.3.5^2.7}\)
Bài 1:Thực hiện phép tính.
1) \(\dfrac{2\cdot6^9-2^5\cdot18^4}{2^2\cdot6^8}\) ; 2)\(\dfrac{15^3+5\cdot15^2-5^3}{18^2+6\cdot18^2-6^3}\)
Bài 2:Tìm x, biết:
1)\(^{\left(5x+1\right)^2}\)=\(\dfrac{36}{49}\) ; 2) \(2^{x-1}=16\) ; 3)\(\left(-\dfrac{3}{4}\right)^{3x-1}=-\dfrac{27}{64}\) ; 4)\(\dfrac{-1}{2}+\dfrac{5}{x+3}=\dfrac{-5}{6}\)
5)\(\dfrac{37-x}{x+13}=\dfrac{3}{7}\) ; 6)\(\dfrac{1}{12}:\dfrac{4}{21}=3\dfrac{1}{2}:\left(3x-2\right)\) ; 7) \(^{2^{2x+1}+4^{x+3}=264}\) ; 8) \(\dfrac{x+7}{-20}=\dfrac{-5}{x+7}\)
9) \(\dfrac{x}{8}=\dfrac{x}{x^3}\) ; 10) \(\dfrac{x-1}{x+5}=\dfrac{6}{7}\)
Mọi người giúp mình với,làm ơn !!!!!
