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NH
1
MC
25 tháng 7 2018
\(a)A=\dfrac{2}{20}+\dfrac{2}{30}+\dfrac{2}{42}+...+\dfrac{2}{240}\)
\(A=2\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{15.16}\right)\)
\(A=2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)
\(A=2\left(\dfrac{4}{16}-\dfrac{1}{16}\right)\)
\(A=\dfrac{2.3}{16}\)
\(=\dfrac{3}{8}\)
\(b)B=\dfrac{5}{6}+\dfrac{11}{12}+\dfrac{19}{20}+\dfrac{29}{30}+\dfrac{41}{42}+\dfrac{55}{56}\)
\(B=\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{12}\right)+...+\left(1-\dfrac{1}{56}\right)\)
\(B=6-\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{7.8}\right)\)
\(B=6-\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{7}-\dfrac{1}{8}\right)\)
\(B=6-\left(\dfrac{4}{8}-\dfrac{1}{8}\right)\)
\(B=\dfrac{48}{8}-\dfrac{3}{8}\)
\(B=\dfrac{45}{8}\)
HT
12 tháng 7 2015
a,\(\frac{7}{x}+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}=\frac{29}{45}\)
\(\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\right)=\frac{29}{45}\)
\(\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{45}\right)=\frac{29}{45}\)
\(\frac{7}{x}+\frac{8}{45}=\frac{29}{45}\)
\(\frac{7}{x}=\frac{29}{45}-\frac{8}{45}=\frac{21}{45}\)
\(\frac{7}{x}=\frac{7}{15}\)
=> x = 15
b,\(\frac{x}{2008}-\left(\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+....+\frac{2}{240}\right)=\frac{5}{8}\)
\(\frac{x}{2008}-2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)=\frac{5}{8}\)
\(\frac{x}{2008}-2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+....+\frac{1}{15}-\frac{1}{16}\right)=\frac{5}{8}\)
\(\frac{x}{2008}-2\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{5}{8}\)
\(\frac{x}{2008}-2.\frac{3}{16}=\frac{5}{8}\)
\(\frac{x}{2008}-\frac{3}{8}=\frac{5}{8}\)
\(\frac{x}{2008}=\frac{5}{8}+\frac{3}{8}=1=\frac{2008}{2008}\)
=> x = 2008
3 tháng 4 2015
A=3/2+13/12+31/30+...+9901/9900
= 1+1/2+1+1/12+1+1/30+...+1+1/9900
=1+1+1+...+1+1(50 cs)+1/2+1/12+1/30+...+1/9900
=50+1/2+1/12+1/30+...+1/9900
B=5/6+19/20+41/42+...+10099/10100
=(1-1/6)+(1-1/20)+(1-1/42)+...+(1-1/10100)
=1+1+...+1(50cs)-1/6-1/20-1/42-...-1/10100
A-B=(50+1/2+1/12+1/30+...+1/9900)-(50-1/6-1/20-1/42-...-1/10100)
=1/2+1/6+1/12+1/20+...+1/9900+1/10100
=1/1.2+1/2.3+1/3.4+1/4.5+...+1/99.100+1/100.101
=1-1/2+1/2-1/3+1/3-1/4+1/4-...+1/99-1/100+1/100-1/101
=1-1/101
=100/101
LX
3
20 tháng 8 2017
\(\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{12}+\dfrac{5}{20}+\dfrac{5}{30}+\dfrac{5}{42}+...+\dfrac{5}{110}\)
\(=\dfrac{5}{1.2}+\dfrac{5}{2.3}+\dfrac{5}{3.4}+\dfrac{5}{4.5}+\dfrac{5}{5.6}+\dfrac{5}{6.7}+...+\dfrac{5}{10.11}\)
\(=\dfrac{5}{1}-\dfrac{5}{2}+\dfrac{5}{2}-\dfrac{5}{3}+\dfrac{5}{3}-\dfrac{5}{4}+\dfrac{5}{4}-\dfrac{5}{5}+...+\dfrac{5}{10}-\dfrac{5}{11}\)
\(=\dfrac{5}{1}-\dfrac{5}{11}=\dfrac{50}{11}\)
DH
20 tháng 8 2017
=5(1/2+1/6+1/12+1/20+1/30+1/42+...+1/110)
=5(1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/10.11)
=5(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/10-1/11)
=5(1-1/11)=5.10/11=50/11
MN
1
NT
0
A = 5/4.5 + 5/5.6 + 5/6.7 +...+ 5/15.16
A = 5/4 - 5/5 + 5/5 - 5/6 + 5/6 - 5/7 +...+ 5/15 - 5/16
A = 5/4 - 5/16
A = 15/16
Nếu sai cho mk xin lỗi tại vì mk học lớp 7 nên quên quên dạng này rồi
ta có :
A = 5/20 + 5/30 + 5/42 + ... + 5/240
A = 5/4.5 + 5/5.6 + 5/6.7 + .... + 5/15.16
A = 5. ( 1/4.5 + 1/5.6 + ....... + 1/15.16)
A = 5. ( 1/4 - 1/5 + 1/5 - 1/6 + ...... + 1/15 - 1/16)
A = 5, ( 1/4 - 1/16 )
A = 5. 3/16
A = 15/16