2/5+3/7=...
1/7+3/7+4/7=(1/7+3/7)+....=1/7+(3/7+...)=(1/7+4/7)+...
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\(A=1+7+7^2+7^3+...+7^{2007}\)
\(7A=7+7^2+7^3+7^4+...+7^{2008}\)
\(7A-A=\left(7+7^2+7^3+7^4+...+7^{2008}\right)-\left(1+7+7^2+7^3+...+7^{2007}\right)\)
\(6A=7^{2008}-1\)
\(A=\frac{7^{2008}-1}{6}\)
Tương tự, \(B=\frac{4^{101}-1}{3},C=\frac{3^{101}-1}{2}\).
\(D=7+7^3+7^5+7^7+...+7^{99}\)
\(7^2.D=7^3+7^5+7^7+7^9+...+7^{101}\)
\(\left(7^2-1\right)D=\left(7^3+7^5+7^7+7^9+...+7^{101}\right)-\left(7+7^3+7^5+7^7+...+7^{99}\right)\)
\(48D=7^{101}-7\)
\(D=\frac{7^{101}-7}{48}\)
Tương tự, \(E=\frac{2^{9011}-2}{3}\)
\(\left(\dfrac{5}{7}-\dfrac{7}{7}\right)-\left[0,2-\left(-\dfrac{2}{7}-\dfrac{1}{10}\right)\right]\)
=\(-\dfrac{2}{7}-\left[\dfrac{1}{5}+\dfrac{2}{7}+\dfrac{1}{10}\right]\)
=\(-\dfrac{2}{7}-\dfrac{1}{5}-\dfrac{2}{7}-\dfrac{1}{10}\)
=\(\left(-\dfrac{2}{7}-\dfrac{2}{7}\right)-\left(\dfrac{1}{5}+\dfrac{1}{10}\right)\)
=\(-\dfrac{4}{7}-\left(\dfrac{2}{10}+\dfrac{1}{10}\right)\)
=\(-\dfrac{4}{7}-\dfrac{3}{10}\)
=\(-\dfrac{40}{70}-\dfrac{21}{70}\)
=\(-\dfrac{61}{70}\)
(3 - \(\dfrac{1}{4}\) + \(\dfrac{2}{3}\)) - (5 - \(\dfrac{1}{3}\) - \(\dfrac{5}{6}\)) - (6 - \(\dfrac{7}{4}\) - \(\dfrac{3}{2}\))
= 3 - \(\dfrac{1}{4}\) + \(\dfrac{2}{3}\) - 5 + \(\dfrac{1}{3}\) + \(\dfrac{5}{6}\) - 6 + \(\dfrac{7}{4}\) + \(\dfrac{3}{2}\)
= (3 - 5 - 6) + ( \(\dfrac{7}{4}\) - \(\dfrac{1}{4}\)) + (\(\dfrac{2}{3}\) + \(\dfrac{1}{3}\)) + \(\dfrac{3}{2}\) + \(\dfrac{5}{6}\)
= - 8 + \(\dfrac{3}{2}\) + 1 + \(\dfrac{3}{2}\) + \(\dfrac{5}{6}\)
= (- 8 + 1) + (\(\dfrac{3}{2}\) + \(\dfrac{3}{2}\)) + \(\dfrac{5}{6}\)
= -7 + 3 + \(\dfrac{5}{6}\)
= - 4 + \(\dfrac{5}{6}\)
= \(\dfrac{-19}{6}\)
a) -1/24 - [ 1/4 - ( 1/2 - 7/8 )]
= -1/24 - [ 1/4 +3/8 ]
= -1/24 - 5/8
= -2/3.
a) -1/24 - [ 1/4 - ( 1/2 - 7/8 )]
= -1/24 - [ 1/4 +3/8 ]
= -1/24 - 5/8
= -2/3.
6 + 1 = 7 5 + 2 = 7 4 + 3 = 7
1 + 6 = 7 2 + 5 = 7 3 + 4 = 7
7 - 6 = 1 7 - 5 = 2 7 - 4 = 3
7 - 1 = 6 7 - 2 = 5 7 - 3 = 4
6+1=7
1+6=7
7-6=1
7-1=6
5+2=7
2+5=7
7-5=2
7-2=5
4+3=7
3+4=7
7-4=3
7-3=4
Lời giải chi tiết:
4 + 3 = 7 | 5 + 2 = 7 | 6 + 1 = 7 |
3 + 4 = 7 | 2 + 5 = 7 | 1 + 6 = 7 |
7 – 4 = 3 | 7 – 5 = 2 | 7 – 6 = 1 |
7 – 3 = 4 | 7 – 2 = 5 | 7 – 1 = 6 |
Lời giải chi tiết:
7 – 4 – 2 = 1 | 7 – 3 – 1 = 3 | 7 – 4 – 1 = 2 |
7 – 5 – 1 = 1 | 7 – 1 – 3 = 3 | 7 – 2 – 4 = 1 |
\(\dfrac{2}{5}+\dfrac{3}{7}=\dfrac{14}{35}+\dfrac{15}{35}=\dfrac{29}{35}\)
\(\dfrac{1}{7}+\dfrac{3}{7}+\dfrac{4}{7}=\left(\dfrac{1}{7}+\dfrac{3}{7}\right)+\dfrac{4}{7}=\dfrac{1}{7}+\left(\dfrac{3}{7}+\dfrac{4}{7}\right)=\left(\dfrac{1}{7}+\dfrac{4}{7}\right)+\dfrac{3}{7}\)