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TD
29 tháng 1 2023
=2x(1/12+1/20+1/30+...+1/3660+1/3782)
=2x(1/(3x4)+1/(4x5)+1/(5x6)+...+1/(60x61)+1/(61x62)
=2x(1/3-1/4+1/4-1/5+1/5-1/6+...+1/60-1/61+1/61-1/62)
=2x(1/3-1/62)=2x59/186=59/93
PC
1
TG
11 tháng 4 2022
1/2 N=1/2x3 + 1/3x4 +...+1/9x10
1/2 N=1/2-1/3+1/3-1/4+...+1/9-1/10
1/2 N=1/2-1/10=2/5
N=2/5:1/2=4/5
PC
1
2 tháng 7 2023
M=2/6+2/12+...+2/90
=2(1/6+1/12+...+1/90)
=2(1/2-1/3+1/3-1/4+...+1/9-1/10)
=2*4/10=8/10=4/5
LM
Lê Minh Vũ
CTVHS
15 tháng 6 2023
3 x 15 + 21 x 15 + 85 x 5
= 45 + 315 + 425
= 785
15 - 30 + 40
= 25
21 + 19 - 50 + 10
= 0
\(\dfrac{1}{5}-\dfrac{1}{4}+2\)
\(=-\dfrac{1}{20}+2\)
\(=\dfrac{39}{20}\)
\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)
\(=\dfrac{5}{12}\times\dfrac{1}{4}\)
\(=\dfrac{5}{12}\times\dfrac{3}{12}\)
\(=\dfrac{5}{48}\)
\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)
\(=-\dfrac{9}{20}\)
BD
15 tháng 6 2023
\(3\times15+21\times15+85\times5\\ =15\times\left(3+21\right)+425\\ =15\times24+425\\ =360+425\\ =785\)
\(15-30+40\\ =\left(15+40\right)-30\\ =55-30\\ =25\)
\(21+19-50+10\\ =\left(21+19\right)-\left(50-10\right)\\ =40-40\\ =0\)
\(\dfrac{1}{5}-\dfrac{1}{4}+2\)
\(=\dfrac{4}{20}-\dfrac{5}{20}+\dfrac{40}{20}\)
\(=\dfrac{\left(4+40\right)}{20}-\dfrac{5}{20}\)
\(=\dfrac{44}{20}-\dfrac{5}{20}\)
\(=\dfrac{39}{20}\)
\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)
\(=\dfrac{5}{12}\times\dfrac{1}{4}\)
\(=\dfrac{5}{48}\)
\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)
\(=\dfrac{2}{20}+\dfrac{4}{20}-\dfrac{15}{20}\)
\(=\dfrac{6}{20}-\dfrac{15}{20}\)
\(=-\dfrac{9}{20}\)
27 tháng 8 2023
\(C\text{=}\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}\)
\(C\text{=}\left(\dfrac{1}{3}+\dfrac{1}{6}\right)+\left(\dfrac{1}{10}+\dfrac{1}{15}\right)+\left(\dfrac{1}{21}+\dfrac{1}{28}\right)\)
\(C\text{=}\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}\)
\(C\text{=}\dfrac{3}{4}\)
LN
1
LD
23 tháng 5 2023
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
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
19 tháng 5 2023
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 = \(\dfrac{16}{9}\)
AH
Akai Haruma
Giáo viên
9 tháng 11 2021
Lời giải:
$\frac{A}{2}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$
$=\frac{2-1}{1\times 2}+\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+\frac{5-4}{4\times 5}+\frac{6-5}{5\times 6}+\frac{7-6}{6\times 7}+\frac{9-8}{8\times 9}+\frac{10-9}{9\times 10}$
$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}$
$=1-\frac{1}{9}=\frac{8}{9}$
$\Rightarrow A=2\times \frac{8}{9}=\frac{16}{9}$
23 tháng 5 2021
B =1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28
B = 1 - 1/3 + 1/3 - 1/6 + 1/6 - 1/10 + 1/10 - 1/15 + 1/15 - 1/21 + 1/21 - 1/28
B = 1 - ( 1/3 + 1/3 - 1/6 + 1/6 - 1/10 + 1/10 - 1/15 + 1/15 - 1/21 + 1/21 ) - 1/28
B = 1 - 1/28
B = 27/28
~ Hok T ~