Question

b1:Cho A= 1+2+2^2+2^3+...+2^2009 và B=2^2010 . So sánh A và B

Bài 2:tính

P=1/2+1/2^2+1/2^3+....+1/2^19+1/2^20

giúp mình vs

Answer 1

\(P=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{19}}+\dfrac{1}{2^{20}}\\ 2P=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{18}}+\dfrac{1}{2^{19}}\\ 2P-P=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{18}}+\dfrac{1}{2^{19}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{19}}+\dfrac{1}{2^{20}}\right)\\ P=1-\dfrac{1}{2^{20}}\)

Answer 2

gúp mình bài 2 thôi nha

Answer 3

2)

\(P=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}\)

\(\Rightarrow2P=1+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{19}}\)

\(\Rightarrow2P-P=\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{19}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}\right)\)

\(\Rightarrow P=1-\dfrac{2}{2^{20}}\)