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ta có số các số hạng là 398-1+1=398 số hạng
a) A=(1-2)+(3-4)+(5-6)+.......+(397-398)
A=(-1)+(-1)+.....+(-1)
có 398/2=199 cặp
vậy A=(-1)*199=-199
\(A=1-2+3-4+5-6+...+397-398\)
\(A=\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+...+\left(397-398\right)\)
\(A=\left(-1\right)+\left(-1\right)+\left(-1\right)+...\left(-1\right)\)
\(A=\left(-1\right)\cdot199\)
\(A=-199\)
\(B=1+3-5-7+9+11-...+393-395-397-399\)( chỗ này mình cố ý viết thêm để dễ nhìn )
\(B=1+\left(3-5-7+9\right)-\left(11-13-15+17\right)-...-\left(387-389-391+393\right)-\left(395-397-399\right)\)
\(B=1+0-0-...-0-\left(-401\right)\)
\(B=1-\left(-401\right)\)
\(B=402\)
a) 2. |1/2-1/3| - 3/2 =1/4 b)3/4-2.|2x-3/2|=2
2.|1/2-1/3|=1/4+3/2 2|2x-3/2|=3/4-2
2.|1/2-1/3|=2/8+12/8 2|2x-3/2|=-5/4
2.|1/2x-1/3|=14/8 |2x-3/2|=-5/4:2
|1/2x-1/3|=14/8:2 |2x-3/2|=-5/8
1/2x-1/3=14/8.2/1 x-3/2=-5/8:2
1/2x-1/3=14/4 x-3/2=-5/16
x-1/3=14/4:1/2 x=-5/16+3/2
x-1/3=14/4.2 x=19/16
x-1/3=7 => x= 19/16 hoặc -19/16
x=7+1/3
x=21/3+1/3
x=22/3
=>x= 22/3 hoăc -22/3
c
g. \(\left(x+\frac{1}{2}\right)\left(\frac{2}{3}-2x\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{2}=0\\\frac{2}{3}-2x=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=\frac{1}{3}\end{cases}}\)
Vậy \(x\in\left\{\frac{-1}{2};\frac{1}{3}\right\}\)
f. \(\frac{2}{3}x-\frac{1}{2}x=\frac{5}{12}\)
\(\Leftrightarrow x\left(\frac{2}{3}-\frac{1}{2}\right)=\frac{5}{12}\)
\(\Leftrightarrow x\left(\frac{4}{6}-\frac{3}{6}\right)=\frac{5}{12}\)
\(\Leftrightarrow\frac{1}{6}x=\frac{5}{12}\)
\(\Leftrightarrow x=\frac{5}{12}\div\frac{1}{6}\)
\(\Leftrightarrow x=\frac{30}{12}=\frac{5}{2}\)
5/8 + 0,2 : |-x/4 + 2/5| = 3/2
0,2 : |-x/4 + 2/5| = 3/2 - 5/8
0,2 : |-x/4 + 2/5| = 7/8
|-x/4 + 2/5| = 7/8 . 0,2
|-x/4 + 2/5| = 7/40
\(\Rightarrow\orbr{\begin{cases}-\frac{x}{4}+\frac{2}{5}=\frac{7}{40}\\-\frac{x}{4}+\frac{2}{5}=-\frac{7}{40}\end{cases}\Rightarrow\orbr{\begin{cases}-\frac{x}{4}=-\frac{9}{40}\\-\frac{x}{4}=-\frac{23}{40}\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{9}{10}\\x=\frac{23}{10}\end{cases}}}\)
Báo cáo sai phạm
5/8 + 0,2 : |-x/4 + 2/5| = 3/2
0,2 : |-x/4 + 2/5| = 3/2 - 5/8
0,2 : |-x/4 + 2/5| = 7/8
|-x/4 + 2/5| = 7/8 . 0,2
|-x/4 + 2/5| = 7/40
⇒[
−x4 +25 =7/40 |
−x4 +25 =−7/40 |
⇒[
−x4 =−9/40 |
−x4 =−23/40 |
⇒[
x=9/10 |
x=2/310 |
Ta có 1/2*3=1/2-1/3;
1/3*4=1/3-1/4
......................(tương tự với các số khác)
1/149*150=1/149-1/150
=>A=1/2-1/3+1/3-1/4+1/4-1/5+...-1/149+1/149-1/150=1/2-1/150
A=75/150-1/150=74/150=37/75
Vậy A= 37/75
A=3.(1/1.2+1/2.3+1/3.4+.....+1/399.400)
A=3.(1/1-1/2+1/2-1/3+......+1/399-1/400)
A=3.(1-1/400)
A=3.399/400
A=1197/400
A=3.(1/1.2+1/2.3+1/3.4+.....+1/399.400)
A=3.(1/1-1/2+1/2-1/3+......+1/399-1/400)
A=3.(1-1/400)
A=3.399/400
A=1197/400
Bài 1: Tính nhanh:
A = 3/1*2 + 3/2*3 + 3/3*4 + ... + 3/399*400
=>3A = 1/1*2 + 1/2*3 + 1/3*4 + ... + 1/399*400
3A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/399 - 1/400
3A = 1 - 1/400
3A = 400/400 - 1/400
3A = 399/400
A = 399/400 : 3
A = 399/400 . 1/3
A = 133/400.
Có gì ko hiểu bn ib mk nha.^^
\(A=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{399.400}\)
\(A=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{399.400}\right)\)
\(A=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{399}-\frac{1}{400}\right)\)
\(A=3.\left(1-\frac{1}{400}\right)\)
\(A=3.\frac{399}{400}\)
\(A=\frac{1197}{400}\)
\(B=\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{399.400}\)
\(B=5.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{399.400}\right)\)
\(B=5.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{399}-\frac{1}{400}\right)\)
\(B=5.\left(1-\frac{1}{400}\right)\)
\(B=5.\frac{399}{400}\)
\(B=\frac{399}{80}\)
\(C=\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{149.151}\)
\(C=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{149}-\frac{1}{151}\)
\(C=\frac{1}{5}-\frac{1}{151}\)
\(C=\frac{146}{755}\)
\(D=\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+...+\frac{3}{149.151}\)
\(D=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{149.151}\right)\)
\(D=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{149}-\frac{1}{151}\right)\)
\(D=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{151}\right)\)
\(D=\frac{3}{2}.\frac{146}{755}\)
\(D=\frac{219}{755}\)
\(E=\frac{11}{1.3}+\frac{11}{3.5}+\frac{11}{5.7}+...+\frac{11}{99.101}\)
\(E=\frac{11}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)
\(E=\frac{11}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(E=\frac{11}{2}.\left(1-\frac{1}{101}\right)\)
\(E=\frac{11}{2}.\frac{100}{101}\)
\(E=\frac{550}{101}\)
_Chúc bạn học tốt_
A= 2/3+2/5-2/9/4/3+4/5-4/9
= 2/3+2/5-8/27+4/5-4/9
= (2/3-8/27-4/9)+(2/5+4/5)
= -2/27+6/5 = 152/135
Ta có: 2/3+2/5-2/9
4/3+4/5-4/9
=2/4.1/3+1/5-1/9
1/3+1/5-1/9
=2/4=1/2
=>A=1/2