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c,Dãy trên có số số hạng là:
(52-2):2+1=26 số hạng
Tổng của dãy trên là:
(52+2).26:2=702
Đáp số :.....
b)0,5x+2/3x+2/3=7/2
1/2x+2/3x+2/3=7/2
x(1/2+2/3)+2/3=7/12
x.7/6+2/3 =7/12
x.7/6 =7/12-2/3
x.7/6 =-1/12
x =-1/12:7/6
x =-1/14
b)3/5-2/15:x=1/2
2/15:x =3/5-1/2
2/15:x =1/10
x =2/15:1/10
x = 4/3
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{\frac{x\times\left(x+1\right)}{2}}=\frac{2015}{2017}\)
\(\Leftrightarrow\frac{1}{2}\)[\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{\frac{x\times\left(x+1\right)}{2}}\)]=\(\frac{1}{2}.\frac{2015}{2017}\)
\(\Leftrightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\times\left(x+1\right)}=\frac{2015}{4034}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2015}{4034}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{n+1}=\frac{2015}{4034}\)\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2015}{4034}=\frac{1}{2017}\)<=> x+1=2017<=>x=2016
A = \(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+..+9\right)}{1\times2+2\times3+3\times4+...+19\times20}\)
\(=\frac{\frac{1\times\left(1+1\right)}{2}+\frac{2\times\left(2+1\right)}{2}+\frac{3\times\left(3+1\right)}{2}...+\frac{9\times\left(9+1\right)}{2}}{1\times2+2\times3+3\times4+...+19\times20}\)
\(=\frac{\frac{1\times2}{2}+\frac{2\times3}{2}+\frac{3\times4}{2}+...+\frac{9\times10}{2}}{1\times2+2\times3+3\times4+...+9\times10}\)
\(=\frac{\frac{1}{2}\times\left(1\times2+2\times3+3\times4+...+9\times10\right)}{1\times2+2\times3+3\times4+...+9\times10}=\frac{\frac{1}{2}}{1}=\frac{1}{2}\)
\(x\times9,6+x:2,5=45\\ x\times9,6+x\times0,4=45\\ x\times\left(9,6+0,4\right)=45\\ x\times10=45\\ x=45:10\\ x=4,5\)
2+3/4=11/4 ; 2-3/5=7/5
5/7:6=5/42 ; 5+2/7=37/7
Bài 2: a) x-1/6=1/2+1/3
x-1/6=5/6
x=5/6+1/6
x=1
b) x+1/8=1/2-1/3
x+1/8=1/6
x=1/6-1/8
x=1/24
c) x:1/2=2/3.3/4
x:1/2=1/2
x=1/2.1/2
x =1/4
15/2 - ( x * 3 ) = 0,2
x * 3 = 15/2 - 0,2
x * 3 = 37,5
x = 37,5 : 3
x = 12,5
2/3 : x - 6 = 1/2
2/3 : x = 1/2 + 6
2/3 : x = 13/2
x = 2/3 : 13/2
x = 4/39