Question

[phạm ngọc hà]

B=

\(\frac{1}{^{5^2}}+\frac{1}{5^4}+\frac{1}{5^6}+......+\frac{1}{5^{^{2014}}}\)

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chứng minh B<1/24

Answer 1

[Trịnh Quỳnh Nhi]

Ta có: \(B=\frac{1}{5^2}+\frac{1}{5^4}+\frac{1}{5^6}+...+\frac{1}{5^{2014}}\)

=> \(25B=1+\frac{1}{5^2}+\frac{1}{5^4}+...+\frac{1}{5^{2012}}\)

=> 25B-B=24B= \(1-\frac{1}{5^{2014}}\)

=> \(B=\frac{1-\frac{1}{5^{2014}}}{24}< \frac{1}{24}\)

=> đpcm