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Đặt an=1+2+3+4+5+...+n
=>an=\(\frac{n\left(n+1\right)}{2}\)
Ta có: Sn=(1+2+3+4+...+n)+(an+1)+(an+2)+(an+3)+...+(an+n)
=an+n.an+an
=an(n+2)
=\(\frac{n\left(n+1\right)}{2}\left(n+2\right)\)
=\(\frac{n\left(n+1\right)\left(n+2\right)}{2}\)
Vậy S100=\(\frac{100.101.102}{2}=515100\)
\(5,\left(x\cdot0,5-\frac{3}{7}\right):\frac{1}{2}=1\frac{1}{7}\)
\(\Leftrightarrow x\cdot0,5:\frac{1}{2}-\frac{3}{7}:\frac{1}{2}=1\frac{1}{7}\)
\(\Leftrightarrow x-\frac{6}{7}=\frac{8}{7}\)
\(\Leftrightarrow x=2\)
\(6,x\cdot1,75=1\frac{3}{10}+45\%\)
\(\Leftrightarrow x\cdot\frac{7}{4}=\frac{13}{10}+\frac{9}{20}\)
\(\Leftrightarrow x\cdot\frac{7}{4}=\frac{7}{4}\)
\(\Leftrightarrow x=1\)
\(7,\frac{5-x}{15}+\frac{5}{12}-\frac{1}{8}=\frac{3}{8}\)
\(\Leftrightarrow\frac{5-x}{15}=\frac{3}{8}-\frac{5}{12}+\frac{1}{8}\)
\(\Leftrightarrow\frac{5-x}{15}=\frac{1}{12}\)
\(\Leftrightarrow60-12x=15\)
\(\Leftrightarrow12x=45\)
\(\Leftrightarrow x=\frac{15}{4}\)
\(8,\left|x-\frac{25}{33}\right|-\frac{3}{11}=\frac{2}{3}\)
\(\Leftrightarrow\left|\frac{x-25}{33}\right|=\frac{31}{33}\)
\(\Rightarrow\orbr{\begin{cases}x-\frac{25}{33}=\frac{31}{33}\\x-\frac{25}{33}=-\frac{31}{33}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{56}{33}\\x=-\frac{2}{11}\end{cases}}\)
\(9,-\frac{9}{8}+\frac{-3}{8}\cdot x=-\frac{1}{8}\)
\(\Leftrightarrow\frac{-9}{8}+\frac{-3}{8}\cdot x+\frac{1}{8}=0\)
\(\Leftrightarrow-1-\frac{3}{8}x=0\)
\(\Leftrightarrow\frac{3}{8}x=-1\)
\(\Rightarrow x=-\frac{8}{3}\)
a) \(\frac{x}{3}-\frac{1}{4}=\frac{-5}{6}\)
\(\Rightarrow\frac{x}{3}=\frac{-5}{6}+\frac{1}{4}\)
\(\Rightarrow\frac{x}{3}=\frac{-7}{12}\)
\(\Rightarrow x=\frac{\left(-7\right).3}{12}\)
\(\Rightarrow x=\frac{-7}{4}\)
Vậy x = \(\frac{-7}{4}\)
b) \(\frac{x+3}{15}=\frac{1}{3}\)
\(\Rightarrow\left(x+3\right).3=15\)
\(\Rightarrow x+3=15:3\)
\(\Rightarrow x+3=5\)
\(\Rightarrow x=5-3\)
\(\Rightarrow x=2\)
Vậy x = 2
c) \(\frac{x-12}{4}=\frac{1}{2}\)
\(\Rightarrow\left(x-12\right).2=4\)
\(\Rightarrow x-12=4:2\)
\(\Rightarrow x-12=2\)
\(\Rightarrow x=2+12\)
\(\Rightarrow x=14\)
Vậy x = 14
d) \(\frac{25}{9}-\frac{12}{13}x=\frac{7}{9}\)
\(\Rightarrow\frac{12}{13}x=\frac{25}{9}-\frac{7}{9}\)
\(\Rightarrow\frac{12}{13}x=2\)
\(\Rightarrow x=2:\frac{12}{13}\)
\(\Rightarrow x=\frac{13}{6}\)
Vậy x = \(\frac{13}{6}\)
_Chúc bạn học tốt_
a)\(\frac{x}{3}-\frac{1}{4}=-\frac{5}{6}\)
\(\frac{x}{3}=-\frac{5}{6}+\frac{1}{4}\)
\(\frac{x}{3}=-\frac{7}{12}\)
\(x=-\frac{7}{12}\times3\)
\(\Rightarrow x=-\frac{7}{4}\)
b) \(\frac{x+3}{15}=\frac{1}{3}\)
\(\frac{x+3}{15\div5}=\frac{1}{3}\)
\(\Rightarrow x=5-3\)
\(\Rightarrow x=2\)
c) \(\frac{x-12}{4}=\frac{1}{2}\)
\(\frac{x-12}{4\div2}=\frac{1}{2}\)
\(x=12+2\)
\(\Rightarrow x=14\)
d) tự làm nhé cũng dễ mà
* x/7 = -6/21
=> x = -6.7 : 21
=> x = -2
* x/-2 = -8/x
=> x.x = -8.(-2) = 16
=> x^2 = 16
=> x = 4 hoặc x = -4