\(B=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^3}{3.4}.\frac{4^2}{4.5}\)
TÍNH GIÁ TRỊ BIỂU THỨC
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(A=\left(\frac{1}{2016}+1\right)+\left(\frac{2}{2015}+1\right)+...+\left(\frac{2015}{2}+1\right)+1\)
= \(\frac{2017}{2016}+\frac{2017}{2015}+\frac{2017}{2014}+...\frac{2017}{2}+\frac{2017}{2017}\)
= \(2017\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}\right)\)
\(\Rightarrow\frac{A}{B}=\frac{2017\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}}\)
= 2017
Chúc bạn học giỏi!
10750 = (10710)5
7375 = (735)5
Mà 10710 > 735 ; 5 = 5
\(\Rightarrow\)10750 > 7375
\(\left(\frac{3}{2}-\frac{1}{2}x\right)\left(x^3-\frac{1}{4}x\right)=0\)
\(\Rightarrow\orbr{\begin{cases}\frac{3}{2}-\frac{1}{2}x=0\left(1\right)\\x^3-\frac{1}{4}x=0\left(2\right)\end{cases}}\)
Giải (1)
\(\frac{3}{2}-\frac{1}{2}x=0\)
\(\frac{1}{2}x=\frac{3}{2}\)
\(x=3\)
Giải (2)
\(x^3-\frac{1}{4}x=0\)
\(x\left(x^2-\frac{1}{4}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x^2-\frac{1}{4}=0\left(3\right)\end{cases}}\)
Giải (3)
\(x^2-\frac{1}{4}=0\)
\(x^2=\frac{1}{4}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-\frac{1}{2}\end{cases}}\)
Vậy, \(x\in\left\{-\frac{1}{2};\frac{1}{2}0;3\right\}\)
\(\left(\frac{3}{2}-\frac{1}{2}x\right).\left(x^3-\frac{1}{4}x\right)=0\)
\(\Rightarrow\orbr{\begin{cases}\frac{3}{2}-\frac{1}{2}x=0\\x^3-\frac{1}{4}x=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}-\frac{1}{2}x=\frac{3}{2}\\x.\left(x^2-\frac{1}{4}\right)=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}\div\frac{-1}{2}\\x=0\div\left(x^2-\frac{1}{4}\right)\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-3\\x=0\end{cases}}\)
vậy x = -3 hoặc x = 0
ta có: 1/2=1/1x2
1/6=1/2x3
1/12=1/3x4
1/20=1/4x5
1/30=1/5x6
1/42=1/6x7
1/56=1/7x8
1/72=1/8x9
1/90=1/9x10
1/110=1/10x11
tiếp theo bn tiếp tục nhé
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110
=1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10+1/10x1
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11
=1-1/11
=10/11
hình như là 32 chứ k f 33
\(B=\frac{1^2}{1\cdot2}\cdot\frac{2^2}{2\cdot3}\cdot\frac{3^2}{3\cdot4}\cdot\frac{4^2}{4\cdot5}\)
\(B=\frac{\left(1\cdot1\right)\left(2\cdot2\right)\left(3\cdot3\right)\left(4\cdot4\right)}{\left(1\cdot2\right)\left(2\cdot3\right)\left(3\cdot4\right)\left(4\cdot5\right)}\)
\(B=\frac{\left(1\cdot2\cdot3\cdot4\right)\left(1\cdot2\cdot3\cdot4\right)}{\left(1\cdot2\cdot3\cdot4\right)\left(2\cdot3\cdot4\cdot5\right)}\)
\(=\frac{1}{5}\)
\(B=\frac{1^2}{1\cdot2}\cdot\frac{2^2}{2\cdot3}\cdot\frac{3^2}{3\cdot4}\cdot\frac{4^2}{4\cdot5}\)
\(B=\frac{1^2\cdot2^2\cdot3^2\cdot4^2}{1\cdot2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5}\)
\(B=\frac{1^2\cdot2^2\cdot3^2\cdot4^2}{1^2\cdot2^2\cdot3^2\cdot4^2\cdot5}=\frac{1}{5}\)