30 đ nha, Help mee, KO SPAM NHA
A = $\frac{1}{2}$ + $\frac{1}{2^2}$ + $\frac{1}{2^3}$ + … + $\frac{1}{2 mũ 2015}$ + $\frac{1}{2 mũ 2016}$
Chứng tở rằng A < 1 [ phải ghi các cách làm ra nhé( cả phân số luôn)]
30 đ nha, Help mee, KO SPAM NHA A = $\frac{1}{2}$ + $\frac{1}{2^2}$ + $\frac{1}{2^3}$ + … + $\frac{1}{2 mũ 2015}$ + $\frac{1}{2 mũ 2016}$ Chứng tở
By Hailey
Giải thích các bước giải:
Ta có : $A = \dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+….+\dfrac{1}{2^{2015}}+\dfrac{1}{2^{2016}}$
$\to 2A =1+ \dfrac{1}{2}+\dfrac{1}{2^2}+….+\dfrac{1}{2^{2014}}+\dfrac{1}{2^{2015}}$
$\to 2A – A = \bigg( 1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+….+\dfrac{1}{2^{2014}}+\dfrac{1}{2^{2015}}\bigg)-\bigg( \dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+….+\dfrac{1}{2^{2015}}+\dfrac{1}{2^{2016}}\bigg)$
$\to A = 1-\dfrac{1}{2^{2016} }< 1$
Vậy $A<1$
A = 1/2 + 1/2^2 +…+ 1/2^2015 + 1/2^2016
2A = 2.(1/2 + 1/2^2 +…+ 1/2^2015 + 1/2^2016)
2A = 1 + 1/2 + … + 1/2^2014 + 1/2^2015
2A – A = (1 + 1/2 + … + 1/2^2014 + 1/2^2015) – (1/2 + 1/2^2 +…+ 1/2^2015 + 1/2^2016)
A = 1 – 1/2^2016
=> A < 1