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PN
3 tháng 7 2017
=> 2(1/15+1/35+1/63+1/99)x=2
=>(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)x=2
=>8/33x=2
=>x=2:8/33
=>x=8,25
DP
3 tháng 7 2017
\(\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\cdot x=1\)
\(\left(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}\right)\cdot x=1\)
\(\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\right]\cdot x=1\)
\(\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{11}\right)\right]\cdot x=1\)
\(\left[\frac{1}{2}\cdot\frac{8}{33}\right]\cdot x=1\)
\(\frac{4}{33}\cdot x=1\)
\(\Rightarrow x=\frac{1}{\frac{4}{33}}=\frac{33}{4}\)
IW
9 tháng 7 2016
\(\Rightarrow A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.....+\frac{1}{99.101}\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{99.101}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{99}-\frac{1}{101}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{101}\right)\)
\(\Rightarrow A=\frac{1}{2}.\frac{88}{303}\)
\(\Rightarrow A=\frac{44}{303}\)
MH
9 tháng 7 2016
\(A=\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+...+\frac{1}{99\times101}\)
\(\Rightarrow2A=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{99\times101}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)
\(=\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)
=> A = 98/203 : 2 = 49/303
14 tháng 7 2016
\(2B=\frac{2}{1.3}+\frac{2}{3.5}+....+\frac{2}{9.11}\)
\(2B=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\)
\(2B=\frac{1}{1}-\frac{1}{11}=\frac{10}{11}\)
\(B=\frac{10}{11}:2=\frac{10}{11}.\frac{1}{2}=\frac{5}{11}\)
14 tháng 7 2016
\(B=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{1}{2}.\frac{10}{11}=\frac{5}{11}\)
NN
18 tháng 8 2017
<=> \(\left(\frac{1}{3\cdot5}+\frac{1}{5.7}+...+\frac{1}{13\cdot15}\right)+x=\frac{17}{15}\)
<=> \(\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-...-\frac{1}{15}\right)+x=\frac{17}{15}\)
<=>\(\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{15}\right)+x=\frac{17}{15}\)
<=> \(\frac{2}{15}+x=\frac{17}{15}\)
=> x = 1
NH
18 tháng 8 2017
(1/3.5+1/5.7+1/7.9+1/9.11+1/11.13+1/13.15)+x=17/15
[2.(1/3-1/5+1/5-1/7+...+1/13-1/15)]+x=17/15
[2.(1/3-1/15)]+x=17/15
(2.4/15)+x=17/15
6/15+x=17/15
x=17/15-6/15
x=11/15
NC
1
3 tháng 2 2016
A = 1/15 + 1/35 + 1/ 63 + 1/99 + ...+ 1/9999
A = 1/(3x5) + 1/(5x7) + 1/(7x9) + 1/(9x11) + ... + 1/(99 x 101)
Ax2 = 2/(3x5) + 2/(5x7) + 2/(7x9) + 2/(9x11) + ... + 2/(99 x 101)
Ax2 = 1/3 – 1/5 + 1/5 – 1/7 + 1/7 – 1/9 + 1/9 – 1/11 + ...+ 1/99 – 1/101
Ax2 = 1/3 – 1/101 = 98/303
A = 98/303 : 2
A = 49/303
tớ không chắc nhé
27 tháng 6 2017
= 1/3 x 5 + 1/5x 7 + 1/7 x 9 +...+1/99 x 101
=1/ 2x (1/3 - 1/5 +1/5 - 1/7 +1/7 - 1/9 + 1/99 - 1/101)
=1/2 x (1/3 - 1/99)
=1/2 x (1/3 - 1/101)
=1/2 x (98/303)
=1/15 + 1/35 + 1/63 +1/99+...+1/9999
=49/303
27 tháng 6 2017
\(=\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{99.101}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(=\frac{1}{3}-\frac{1}{101}+0+...+0\)
\(=\frac{98}{303}\)
EF
2
MP
25 tháng 1 2016
A=1/3.5+1/5.7+1/7.9+...+1/99.101
2A= 2/3.5+2/5.7+2/7.9+...+2/99.101
2A= 1/3-1/5+1/5-1/7-1/7+1/7-1/9+...+1/99-1/101
2A=1/3-1/101=98/303
A=(98/303)/2=49/303
Ta có: \(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\cdots+\frac{1}{483}+\frac{1}{575}\)
\(=\frac{1}{3\times5}+\frac{1}{5\times7}+\cdots+\frac{1}{23\times25}\)
\(=\frac12\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+\cdots+\frac{2}{23\times25}\right)\)
\(=\frac12\times\left(\frac13-\frac15+\frac15-\frac17+\cdots+\frac{1}{23}-\frac{1}{25}\right)\)
\(=\frac12\times\left(\frac13-\frac{1}{25}\right)=\frac12\times\frac{22}{75}=\frac{11}{75}\)
hỏi chat gpt là ra
A = \(\frac{1}{15}\) + \(\frac{1}{35}+\frac{1}{63}\) + \(\frac{1}{99}\) + ... + \(\frac{1}{483}\) + \(\frac{1}{575}\)
A = \(\frac12\)x ( \(\frac{2}{3\times5}\) + \(\frac{2}{5\times7}\) + \(\frac{2}{7\times3}\) + \(\frac{2}{9\times11}\) + ... + \(\frac{2}{21\times23}\) +\(\frac{2}{23\times25}\))
A = \(\frac12\)x(\(\frac13\) - \(\frac15\) + \(\frac15\) - \(\frac17\) + ... + \(\frac{1}{21}-\frac{1}{23}\) + \(\frac{1}{23}\) - \(\frac{1}{25}\))
A = \(\frac12\)x(\(\frac13\) - \(\frac{1}{25}\))
A = \(\frac12\)x(\(\frac{25}{75}-\frac{3}{75}\))
A= \(\frac12\times\) \(\frac{22}{75}\)
A = \(\frac{11}{75}\)
gemini