1+1-2-4-56-7+10000-29=?
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a, \(\dfrac{62}{7}.x=\dfrac{29}{90}.\dfrac{3}{56}\)
\(\dfrac{62}{7}.x=\dfrac{29}{1680}\)
\(x=\dfrac{29}{1680}:\dfrac{62}{7}\)
\(x=\dfrac{29}{14880}\)
b, \(\dfrac{1}{5}:x=\dfrac{1}{5}-\dfrac{1}{7}\)
\(\dfrac{1}{5}:x=\dfrac{2}{35}\)
\(x=\dfrac{1}{5}:\dfrac{2}{35}\)
\(x=\dfrac{7}{2}\)
c, \(\left(x+\dfrac{1}{4}-\dfrac{1}{3}\right):\left(2+\dfrac{1}{6}-\dfrac{1}{4}\right)=\dfrac{7}{46}\)
\(\left(x+\dfrac{1}{4}-\dfrac{1}{3}\right):\left(\dfrac{13}{6}-\dfrac{1}{4}\right)=\dfrac{7}{46}\)
\(\left(x+\dfrac{1}{4}-\dfrac{1}{3}\right):\dfrac{23}{12}=\dfrac{7}{46}\)
\(\left(x+\dfrac{-1}{12}\right):\dfrac{23}{12}=\dfrac{7}{46}\)
\(\left(x+\dfrac{-1}{12}\right)=\dfrac{7}{46}.\dfrac{23}{12}\)
\(x+\dfrac{-1}{12}=\dfrac{7}{24}\)
\(x=\dfrac{7}{24}-\dfrac{-1}{12}\)
\(x=\dfrac{3}{8}\)
\(A=\frac{1}{1\cdot2}+\frac{2}{2\cdot4}+\frac{3}{4\cdot7}+\frac{4}{7\cdot11}+...+\frac{10}{46\cdot56}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{46}-\frac{1}{56}\)
\(A=1-\frac{1}{56}\)
\(A=\frac{55}{56}\)
\(B=\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+\frac{4}{11\cdot15}+...+\frac{4}{23\cdot27}\)
\(B=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{23}-\frac{1}{27}\)
\(B=\frac{1}{3}-\frac{1}{27}\)
\(B=\frac{8}{27}\)
\(C=\frac{4}{3\cdot6}+\frac{4}{6\cdot9}+\frac{4}{9\cdot12}+...+\frac{4}{99\cdot102}\)
\(C=\frac{4}{3}\left(\frac{3}{3\cdot6}+\frac{3}{6\cdot9}+\frac{3}{9\cdot12}+...+\frac{3}{99\cdot102}\right)\)
\(C=\frac{4}{3}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{99}-\frac{1}{102}\right)\)
\(C=\frac{4}{3}\left(\frac{1}{3}-\frac{1}{102}\right)\)
\(C=\frac{4}{3}\cdot\frac{33}{102}\)
\(C=\frac{22}{51}\)
1+2+3+....+10000
Số số hạng của tổng là:
(10000-1):1+1=10000 ( số )
Tổng là:
(10000+1)x10000:2=50005000
2+4+6+8+10+.....+10000
Số số hạng của tổng là:
(10000-2):2+1=5000( số )
Tổng là:
(10000+2)x5000:2=25005000
1: \(=\dfrac{1}{29\cdot30}-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{28\cdot29}\right)\)
\(=\dfrac{1}{29\cdot30}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{28}-\dfrac{1}{29}\right)\)
\(=\dfrac{1}{29\cdot30}-\dfrac{28}{29}=\dfrac{1-28\cdot30}{870}=\dfrac{-859}{870}\)
\(1+1+1+1+1+1+1+....+1\)
\(=1.10000\)
\(=10000\)
\(2+2+2+2+2+2+2+....+2\)
\(=2.10000\)
\(=20000\)
\(0+1+2+3+4+5+6+7+8+9+.....+10000\)
Số số hạng của dãy là:
(10000-0):1+1=10001( số )
Tổng của dãy là:
(10000+0).10001:2=50005000
1+1-2-4-56-7+10000-29=9904