Tìm x là số tự nhiên biết:
\(2x:\left(1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+x}\right)=2020\)
a. Tìm giá trị nhỏ nhất của biểu thức sau:
\(\left(\frac{2x}{3}+\frac{1}{2}\right)^3-\left(\frac{2x}{3}-\frac{1}{2}\right)^3+\left(\frac{1}{2x}+1\right)\left(\frac{1}{2x}-1\right)-\frac{1}{12}x^2-3x\)
b. Tìm số tự nhiên abc biết: 3a + 4b =7c và a, b, c đôi một khác nhau
1/tìm \(x\in Z\)biết \(38-\left(|x+10|+13\right)=\left(-6\right)^{20}:\left(9^9\times4^{10}\right)\)
2/tìm số tự nhiên x biết rằng \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^x+1}=\frac{2047}{2048}\)
3/\(x\inℕ^∗\)biết \(M=111...1\)(2x chữ số 1) \(-777...7\)(x chữ số 7) là số chính phương
a,cho các số x,y,z khác 0 thoả mãn
\(x-2y+\frac{z}{y}=z-2x+\frac{y}{x}=x-2z-\frac{y}{z}\).Tính giá trị biểu thức A=\(\left(1+\frac{y}{x}\right)\times\left(1+\frac{y}{x}\right)=\left(1+\frac{x}{z}\right)+2020\)
b, tìm các số tự nhiên x,y thoả mãn xy+4x=35+5y
c, tìm các số tự nhiên x,y thoả mãn 2^/x/+y^2+y=2x+1
Tìm x, biết :
\(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{\left(2x-2\right).}2x=\frac{11}{84}\)
(x là số tự nhiên, x > hoặc = 2
Tìm số tự nhiên x biết:
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{2}{x.\left(x+1\right)}=\frac{1999}{2001}\)
\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{2}{x.\left(x+1\right)}\)
Đặt A=1/3+1/6+1/10+...+2/x*(x+1)
1/2A=1/3*2+1/6*2+1/10*2+...+2/2*x*(x+1)
1/2A=1/6+1/12+1/20+...+1/x*(x+1)
1/2A=1/2*3+1/3*4+1/4*5+...+1/x*(x+1)
1/2A=1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/(x+1)
1/2A=1/2-1/x+1
A=(1/2-1/x+1):1/2
A=1-2/x+1
Ta có A=1999/2001
Hay 1-2/x+1=1999/2001
2/x+1=1-1999/2001
2/x+1=2/2001
=>x+1=2001
=>x=2000
Cho A = 1/3+1/6+1/10+...+2/x(x+1)
1/2A= 1/3.2+1/6.2+1/10.2+...+2/x(x+1)2
1/2A= 1/6+1/12+1/20+...+1/x(x+1)
1/2A= 1/2.3+1/3.4+1/4.5+...+1/x(x+1)
1/2A= 1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1
1/2A= 1/2-1/x+1
A = (1/2-1/x+1)/1/2
A = 1-2/x+1
Mà A=1999/2001
=> 1-2/x+1= 1999/2001
2/x+1= 1-1999/2001
2/x+1= 2/2001
=>x+1=2001
=>x = 2000
Đặt N=1/10+1/15+1/21+...+2/x*(x+1)
1/2N=1/20+1/30+1/42+...+1/x*(x+1)
1/2N=1/4*5+1/5*6+1/6*7+...+1/x*(x+1)
1/2N=1/4-1/5+1/5-1/6+1/6-1/7+...+1/x-1/x+1
1/2N=1/4-1/x+1
N=(1/4-1/x+1):1/2
N=1/2-2/x+1
Thiếu đề
Tìm số tự nhiên x biết \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=1\frac{2003}{2005}\)
\(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=1\frac{2003}{2005}\)
\(\frac{2}{2}+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{4008}{2005}\)
\(2.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{x\left(x+1\right)}\right)=\frac{4008}{2005}\)
\(2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{4008}{2005}\)
\(=>2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{4008}{2005}\)
\(2.\left(1-\frac{1}{x+1}\right)=\frac{4008}{2005}\)
=> \(1-\frac{1}{x+1}=\frac{4008}{2005}:2=\frac{2004}{2005}\)
\(\frac{1}{x+1}=1-\frac{2004}{2005}=\frac{1}{2005}\)
=>x+1=2005
=>x=2004
1/3 + 1/6 + 1/10 +...+ 2/x(x+1) = 2014/2015
Đ/A là 2004
chúc đồng chí Chế Minh Hải học tốt
\(M=\left(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{2020^2}\right)X\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2020^2}\right)-\left(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2020^2}\right)X\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2020^2}\right)\)Làm nhanh và ngắn gọn nhất có thể nhé ! mình tik cho 10 tik
\(M=\left(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2020^2}\right)\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2020^2}\right)-\left(\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2020^2}\right)\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2020^2}\right)\)
\(M=\left(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2020^2}\right)\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2020^2}\right)(1-1)\)
\(M=\left(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2020^2}\right)\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2020^2}\right).0\)
\(M=0\)
Vì số bị trừ và số trừ gồm hai tích đảo ngược nhau nên M=0
Tìm số tự nhiên x biết rằng : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2007}{2009}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2007}{2009}\)
\(\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2007}{2009}\)
\(\Rightarrow2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2007}{2009}\)
\(\Rightarrow2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2007}{2009}\)
\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2007}{2009}\)
\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2007}{2009}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2007}{2009}\div2\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2007}{4018}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2007}{4018}\)
\(\Rightarrow\frac{1}{x+1}=\frac{2}{4018}=\frac{1}{2009}\)
\(\Rightarrow x+1=2009\)
\(\Rightarrow x=2008\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2007}{2009}\)
=>\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{2007}{4018}\)(nhân cả hai vế với \(\frac{1}{2}\))
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\)= \(\frac{2007}{4018}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2007}{4018}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2007}{4018}\)
\(\frac{1}{x+1}\)=\(\frac{1}{2}-\frac{2007}{4018}\)
\(\frac{1}{x+1}=\frac{1}{2009}\)
x+1=2009
x=2009-1=2008
Vậy x bằng 2008
Tìm số tự nhiên x, biết:
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.....+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{15}{93}\)
2/3.5+2/5.7+2/7.9+...+2/(2x+1)(2x+3)=2.15/93
1/3-1/5+1/5-1/7+...+1/2x+1-1/2x+3=10/31
1/3-1/2x+3=10/31
1/(2x+3)=1/93
2x+3=93
2x=90
x=45