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S1/2=1/2+1/6+1/12+...+1/600
S1/2=1/1*2+1/2*3+....+1/24*25
S1/2=1-1/25
S1/2=24/25
S=48/25
3 x 15 + 21 x 15 + 85 x 5
= 45 + 315 + 425
= 785
15 - 30 + 40
= 25
21 + 19 - 50 + 10
= 0
\(\dfrac{1}{5}-\dfrac{1}{4}+2\)
\(=-\dfrac{1}{20}+2\)
\(=\dfrac{39}{20}\)
\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)
\(=\dfrac{5}{12}\times\dfrac{1}{4}\)
\(=\dfrac{5}{12}\times\dfrac{3}{12}\)
\(=\dfrac{5}{48}\)
\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)
\(=-\dfrac{9}{20}\)
\(3\times15+21\times15+85\times5\\ =15\times\left(3+21\right)+425\\ =15\times24+425\\ =360+425\\ =785\)
\(15-30+40\\ =\left(15+40\right)-30\\ =55-30\\ =25\)
\(21+19-50+10\\ =\left(21+19\right)-\left(50-10\right)\\ =40-40\\ =0\)
\(\dfrac{1}{5}-\dfrac{1}{4}+2\)
\(=\dfrac{4}{20}-\dfrac{5}{20}+\dfrac{40}{20}\)
\(=\dfrac{\left(4+40\right)}{20}-\dfrac{5}{20}\)
\(=\dfrac{44}{20}-\dfrac{5}{20}\)
\(=\dfrac{39}{20}\)
\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)
\(=\dfrac{5}{12}\times\dfrac{1}{4}\)
\(=\dfrac{5}{48}\)
\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)
\(=\dfrac{2}{20}+\dfrac{4}{20}-\dfrac{15}{20}\)
\(=\dfrac{6}{20}-\dfrac{15}{20}\)
\(=-\dfrac{9}{20}\)
A = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) + \(\dfrac{1}{21}\) + \(\dfrac{1}{28}\) + \(\dfrac{1}{36}\)
A = 2\(\times\) ( \(\dfrac{1}{2}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\) + \(\dfrac{1}{42}\) + \(\dfrac{1}{56}\)+ \(\dfrac{1}{72}\))
A =2\(\times\)( \(\dfrac{1}{1\times2}\)+\(\dfrac{1}{2\times3}\)+\(\dfrac{1}{3\times4}\)+\(\dfrac{1}{4\times5}\)+\(\dfrac{1}{5\times6}\)+\(\dfrac{1}{6\times7}\)+\(\dfrac{1}{7\times8}\)+\(\dfrac{1}{8\times9}\))
A = 2 \(\times\) ( \(\dfrac{1}{1}\)- \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\)+\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+...+\(\dfrac{1}{8}\)-\(\dfrac{1}{9}\))
A = 2\(\times\)( 1 - \(\dfrac{1}{9}\))
A = 2 \(\times\) \(\dfrac{8}{9}\)
A = \(\dfrac{16}{9}\)
Đặt X=phép tính trên
Ta có X=X x 1/2 :1/2
X=(1/6+1/12+...+1/6480):1/2
X=(1/2x3+1/3x4+...+1/80x81):1/2
X=(1/2-1/3+1/3-1/4+...+1/80-1/81):1/2
X=(1/2-1/81):1/2
Đến đây bạn tự tính nhé!!!
Đặt: A=...
\(\frac{A}{2}=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{6480}\)
\(\frac{A}{2}=\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+...+\frac{1}{80x81}\)
\(\frac{A}{2}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{80}-\frac{1}{81}\)
\(\frac{A}{2}=\frac{1}{2}-\frac{1}{81}=\frac{79}{162}\) => A=\(\frac{79}{81}\)
1/3 + 1/6 + 1/10+ ....+1/300
=2/6 + 2/12 + 2/20+ .....+2/600
=2*(1/2*3 + 1/3*4 + 1/4*5 + ...+ 1/24*25)
=2*(1/2 - 1/3 + 1/3 -1/4 +1/4 -1/5 +...+ 1/24 - 1/25)
=2*(1/2 - 1/24)
=2*(12/24 - 1/24)
=2 * 11/24
=11/12