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10^10 .(-10^4)
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\(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)
\(=\left(\dfrac{1}{10}+\dfrac{9}{10}\right)+\left(\dfrac{2}{10}+\dfrac{8}{10}\right)+\left(\dfrac{3}{10}+\dfrac{7}{10}\right)+\left(\dfrac{4}{10}+\dfrac{6}{10}\right)+\dfrac{5}{10}\)
\(=1+1+1+1+\dfrac{5}{10}\)
\(=4+\dfrac{5}{10}\)
\(=\dfrac{45}{10}\)
\(13,25:0,5+13,25:0,25+13,25:0,125+13,25\times6\)
\(=13,25:\dfrac{1}{2}+13,25:\dfrac{1}{4}+13,25:\dfrac{1}{8}+13,25\times6\)
\(=13,25\times2+13,25\times4+13,25\times8+13,25\times6\)
\(=13,25\times\left(2+4+8+6\right)\)
\(=13,25\times20\)
\(=265\)
\(\frac{10}{3.8}+\frac{10}{8.13}+\frac{10}{13.18}+...+\frac{10}{98.103}\)
= \(2.\left(\frac{5}{3.8}+\frac{5}{8.13}+\frac{5}{13.18}+...+\frac{5}{98.103}\right)\)
= \(2.\left(\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+...+\frac{1}{98}-\frac{1}{103}\right)\)
= \(2.\left(\frac{1}{3}-\frac{1}{103}\right)\)
= \(2.\frac{100}{309}\)
= \(\frac{200}{309}\)
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10/3x8 + 10/8x13 + 10/13x18 + ... + 10/98x103
= 2x(1/3 - 1/8 + 1/8 - 1/13 + 1/13 - 1/18 + ... + 1/98 - 1/103)
= 2x(1/3 - 1/103)
= 2x100/309
= 200/309
\(4\frac{1}{10}+4\frac{2}{10}+4\frac{3}{10}+4\frac{4}{10}\)
= \((4+4+4+4)+(\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+\frac{4}{10})\)
= \(4\times4+\frac{1}{10}(1+2+3+4)\)
= \(16+\frac{1}{10}.10\)
= \(16+1=17\)
3,95 x 1/4 + 3,95 x 9,85 - 3,95 : 10
= 3,95 x 0,25 + 3,95 x 9,85 - 3,95 x 0,1
= 3,95 x ( 0,25 + 9,85 - 0,1 )
= 3,95 x 10
= 39,5
\(A=\frac{10}{56}+\frac{10}{146}+\frac{10}{210}+...+\frac{10}{100}\)
\(10A=\frac{1}{7\cdot8}+\frac{1}{2\cdot73}+\frac{1}{2\cdot105}+...+\frac{1}{10\cdot10}\)
\(10A=\frac{1}{7}-\frac{1}{8}+\frac{1}{2}-\frac{1}{73}+\frac{1}{2}-\frac{1}{105}+...+\frac{1}{10}-\frac{1}{10}\)
\(10A=\frac{1}{7}-\frac{1}{10}\)
\(10A=\frac{3}{70}\)
\(A=\frac{3}{70}:10\)
\(A=\frac{3}{700}\)
\(\dfrac{9}{10}\times2+3\times\dfrac{9}{10}+\dfrac{9}{10}:\dfrac{1}{5}\)
\(=\dfrac{9}{10}\times2+\dfrac{9}{10}\times3+\dfrac{9}{10}\times5\)
\(=\dfrac{9}{10}\times\left(2+3+5\right)\)
\(=\dfrac{9}{10}\times10\)
\(=\dfrac{90}{10}\)
\(=9\)
\(A=1+2+2^2+2^3+...+2^{2020}\)
\(2A=2+2^2+2^3+2^4+...+2^{2021}\)
\(2A-A=\left(2+2^2+2^3+2^4+....+2^{2021}\right)-\left(1+2+2^2+2^3+...+2^{2020}\right)\)
\(A=2^{2021}-1\)
1010 .(-104)
= -(1010 .104)
= -(1014)
= -(10.10.10.10.10.10.10.10.10.10.10.10.10.10)
= -100000000000000