cmr\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\) <3
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CMR:
\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}
Đặt A=\(\frac{1}{2}\) - \(\frac{1}{4}\) + \(\frac{1}{8}\) - \(\frac{1}{16}\) + \(\frac{1}{32}\) - \(\frac{1}{64}\)
=> 2A= 1-\(\frac{1}{2}\) + \(\frac{1}{4}\) - \(\frac{1}{8}\) + \(\frac{1}{16}\) - \(\frac{1}{32}\)
=> 3A= 1 - \(\frac{1}{64}\) <1 => A<1:3 => A<\(\frac{1}{3}\) => đpcm.
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\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\)
\(=\frac{2}{4}-\frac{1}{4}+\frac{2}{16}-\frac{1}{16}+\frac{2}{64}-\frac{1}{64}\)
\(=\frac{1}{2}+\frac{1}{16}+\frac{1}{64}\)
=37/64
Bạn ghi sai đề rồi nhé Biểu thức trên phải lớn hơn 1/3 chứ
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Đặt biểu thức trên là S
Ta có: S= 1/2 - 1/4 + 1/8 -1/16 + 1/32 -1/64
S=1/21 - 1/22 + 1/23 - 1/24 + 1/25 - 1/26
2S=1 - 1/2 + 1/22 - 1 /23 + 1/24 - 1/25
2S+S = 1-1/26
S = 21/64
Vì 21/64< 1/3
nên S<1/3 (dpcm)
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CMR
\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}< \frac{1}{3}\)
CMR: \(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}<\frac{1}{3}\)
đặt A bằng dãy trên
quy đồng mẫu số vs mẫu chung là 64. Ta có A=21/64<21/63=1/3
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CMR:
a, \(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}< \frac{1}{3}\)
b, \(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+.....+\frac{99}{3^{99}}-\frac{100}{3^{100}}< \frac{3}{16}\)
CMR
a)\(\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}-\frac{1}{64}< \frac{1}{3}\)
b)\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+....+\frac{99}{3^{99}}-\frac{100}{3^{100}}< \frac{3}{16}\)
\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\)<\(\frac{1}{3}\)
cmr
CMR: \(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}< \frac{1}{3}\)\(\frac{1}{3}\)
CMR:
a) \(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}<\frac{1}{3}\)
b) \(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}<\frac{3}{16}\)
a)
\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-...-\frac{1}{64}=\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-...-\frac{1}{2^6}=A\)
2A = 1 - \(\frac{1}{2}+\frac{1}{2^2}-...-\frac{1}{2^5}\)
2A + A = 1 - \(\frac{1}{2}+\frac{1}{2^2}-...-\frac{1}{2^5}+\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-\frac{1}{2^4}-...-\frac{1}{2^6}\)
3A = \(1-\frac{1}{2^6}=\frac{2^6-1}{2^6}\)(đpcm)
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CMR:
a)\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}<\frac{1}{3}\)
b)\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}<\frac{3}{16}\)