Toán 8

T

trinhminh18

Ta có :
A=$\dfrac{1}{2}$+$\dfrac{1}{2^2}$+$\dfrac{1}{2^3}$+...+$\dfrac{1}{2^{2014}}$
$\dfrac{1}{2}$.A =1+$\dfrac{1}{2^2}$+$\dfrac{1}{2^3}$+...+
$\dfrac{1}{2^{2015}}$
\RightarrowA-$\dfrac{1}{2}$.A=$\dfrac{1}{2}$-$\dfrac{1}{2^{2015}}$
$\dfrac{1}{2}$.A=$\dfrac{2^{2014}-1}{2^{2015}}$
\RightarrowA=$\dfrac{2^{2015}-2}{2^{2015}}$<1
\Rightarrow$A+1<2$(điều phải c/m)
 
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