1/4.2/6.3/8...15/32=2^x. Tìm x
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SB
2
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10 tháng 6 2016
\(\frac{1}{4}\times\frac{2}{6}\times\frac{3}{8}\times...\times\frac{30}{62}\times\frac{31}{64}=2^x\)
\(\Rightarrow\) \(\frac{1\times2\times3\times...\times30\times31}{4\times6\times8\times...\times62\times64}=2^x\)
\(\Rightarrow\frac{1}{2^{31}}=2^x\)\(\Rightarrow1=2^x\times2^{31}\)
\(\Rightarrow2^{x+31}=2^0\)
\(\Rightarrow x+31=0\Rightarrow x=\left(-31\right)\)
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TK
2
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19 tháng 8 2017
(1.2.3.4.5....31)/(2(1.2.3.4.5.....31).64)=2x
1/(2.64)=2x
1/128=2x
2-7=2x
=>x=-7
NH
0
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NV
0
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\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}....\frac{15}{32}=\frac{1}{2}.\frac{1}{2}.\frac{1}{2}.\frac{2}{3}.\frac{1}{2}.\frac{3}{4}....\frac{1}{2}.\frac{15}{16}\)
\(=\left(\frac{1}{2}.\frac{1}{2}.....\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{15}{16}\right)\)
Số số \(\frac{1}{2}\)là (15-1):1+1=15 số
Do đó \(\left(\frac{1}{2}.\frac{1}{2}.....\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{15}{16}\right)=\left(\frac{1}{2}\right)^{15}.\frac{1.2.3....15}{2.3.4....15.16}\)
\(=\frac{1}{2^{15}}.\frac{1}{16}=\frac{1}{2^{15}}.\frac{1}{2^4}=\frac{1}{2^{15+4}}=\frac{1}{2^{19}}\)
\(\Rightarrow2^x=\frac{1}{2^{19}}\)
\(\Rightarrow x=-19\)