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S=(1-2)+(3-4)+(5-6)+...+(199-200)
S=(-1)+(-1)+...+(-1)
S=(-1).100=-100
S=1+(2-3)+(-4+5)+...+(98-99)+(-100+101)
S=1+(-1)+1+..+(-1)+1
S=1+25.(-1)+25.1
S=1+(-25)+25
S=1+0
=1
1. 3A = 3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101
=> 3A - A = (3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101) - (3 + 3^2 + 3^3 + 3^4 + ... + 3^100 )
=> 2A = 3^101 - 3 => 2A + 3 = 3^101 vậy n = 101
2. 2A = 8 + 2 ^ 3 + 2^4 + ... + 2^20 + 2^21
=> 2A - A = (8 + 2 ^ 3 + 2^4 + ... + 2^20 + 2^21) - (4+ 2^2 + 2 ^ 3 + 2^4 + ... + 2^20 )
=> A = 2^21 là một lũy thừa của 2
3.
a) 3A = 3 + 3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101
=> 3A - A = (3 + 3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101) - (1 + 3 + 3 ^2 + 3 ^ 3 + ... + 3 ^100)
=> 2A = 3^101 - 1 => A = (3^101 - 1)/2
b) 4B = 4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 + 4^ 101
=> 4B - B = (4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 + 4^ 101) - (1 + 4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 )
=> 3B = 4^101 - 1 => B = ( 4^101 - 1)/2
c) xem lại đề ý c xem quy luật như thế nào nhé.
d) 3D = 3^101 + 3^ 102 + 3^ 103 + ... + 36 150 + 3^ 151
=> 3D - D = (3^101 + 3^ 102 + 3^ 103 + ... + 36 150 + 3^ 151) - (3 ^100 + 3 ^ 101 + 3 ^ 102 + .... + 3 ^ 150)
=> 2D = 3^ 151 - 3^100 => D = ( 3^ 151 - 3^100)/2
\(\left(-\frac{15}{22}\div-\frac{5}{11}\right)\cdot\frac{2}{3}\)
\(=\left(-\frac{15}{22}\cdot-\frac{11}{5}\right)\cdot\frac{2}{3}\)
\(=-\frac{3}{2}\cdot\frac{2}{3}\)
\(=-1\)
\(-\frac{1}{2}+\frac{2}{3}-\frac{3}{4}+\frac{4}{5}\)
\(=\left(-\frac{1}{2}-\frac{3}{4}\right)+\left(\frac{2}{3}+\frac{4}{5}\right)\)
\(=\left(-\frac{2}{4}-\frac{3}{4}\right)+\left(\frac{10}{15}+\frac{12}{15}\right)\)
\(=\left(\frac{-2-3}{4}\right)+\left(\frac{10+12}{15}\right)\)
\(=\left(\frac{-5}{4}\right)+\left(\frac{22}{15}\right)\)
\(=\frac{-75}{60}+\frac{88}{60}\)
\(=\frac{-75+88}{60}\)
\(=\frac{13}{60}\)
Mình ghi rõ từng chi tiết rồi nha , chúc bạn học tốt !!!
5/6 - 7/4 .|-2x - 3/2| = 7/12
7/4 .|-2x - 3/2| = 5/6 - 7/12
7/4.|-2x - 3/2| = 1/4
|-2x- 3/2| = 1/4 : 7/4
|-2x - 3/2| = 1/7
\(\Rightarrow\orbr{\begin{cases}-2x-\frac{3}{2}=\frac{1}{7}\\-2x-\frac{3}{2}=-\frac{1}{7}\end{cases}}\Rightarrow\orbr{\begin{cases}-2x=\frac{23}{14}\\-2x=\frac{19}{14}\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{23}{28}\\x=-\frac{19}{28}\end{cases}}\)
\(0,5.\left[\frac{4}{3}.\left(-20\right)\right].0,75.\frac{8}{-35}\)
\(\frac{5}{10}.\left[\frac{4}{3}.\left(-20\right)\right].\frac{75}{100}.\frac{8}{-35}\)
\(=\frac{2}{5}.\left[\frac{4}{3}.\left(-20\right)\right].\frac{3}{4}.\frac{8}{-35}\)
\(=\left(\frac{4}{3}.\frac{3}{4}\right).\left[\frac{2}{5}.\frac{\left(-35\right)}{8}\right].\left(-20\right)\)
\(=1.\left(\frac{2}{1}.\frac{1}{4}\right).\left(-20\right)\)
\(=1.\frac{1}{2}.\left(-20\right)=-\frac{20}{2}=\frac{10}{1}=10\)
Mk ko chắc, bn tham khảo nha
\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}=\frac{50-1}{100}=\frac{49}{100}\)
1/2*3+1/3*4+.....+1/99*100
=1/2-1/3+1/3-1/4+........1/99*100
=1/2+(-1/3+1/3)+(-1/4+1/4)+.........+(-1/99+1/99)-1/100
=1/2-1/100
=50/100-1/100
=49/100
\(\frac{7}{6}+\frac{5}{6}:5-\frac{3}{8}.\left(-3\right)^2\)
\(=\frac{7}{6}+\frac{5}{6}.\frac{1}{5}-\frac{3}{8}.9\)
\(=\frac{7}{6}+\frac{1}{6}-\frac{27}{8}\)
\(=\frac{8}{6}-\frac{27}{8}\)
\(=\frac{32}{24}-\frac{81}{24}\)
\(=\frac{-49}{24}\)
Chúc bạn học tốt !!!
\(\frac{4}{3}B=-1+\frac{3}{4}-\left(\frac{3}{4}\right)^2+...+\left(\frac{3}{4}\right)^{99}\)
\(B=-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+...+\left(\frac{3}{4}\right)^{100}\)
\(\Rightarrow\)\(\frac{7}{3}B=-1+\left(\frac{3}{4}\right)^{100}\Rightarrow B=\frac{\left(\frac{3}{4}\right)^{100}-1}{\frac{7}{3}}=\frac{3\left[\left(\frac{3}{4}\right)^{100}-1\right]}{7}\)
Như vầy đủ gọn chưa bạn?