Question

C=5122512/2²-512/2³-512/2⁴-...-512/2¹⁰

Answer 1

\(C=\dfrac{5122512}{2^2}-512\left(\dfrac{1}{2^3}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{10}}\right)\)

Đặt BT trong ngoặc đơn là B

\(\Rightarrow2B=\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^9}\)

\(B=2B-B=\dfrac{1}{2^2}-\dfrac{1}{2^{10}}\)

\(\Rightarrow C=\dfrac{5120512+2000}{2^2}-512\left(\dfrac{1}{2^2}-\dfrac{1}{2^{10}}\right)=\)

\(=\dfrac{512.10001+2^2.500}{2^2}-512\left(\dfrac{1}{2^2}-\dfrac{1}{2^{10}}\right)=\)

\(=\dfrac{2^9.10001+2^2.500}{2^2}-2^9\left(\dfrac{1}{2^2}-\dfrac{1}{2^{10}}\right)=\)

\(=2^7.10001+500-2^7+\dfrac{1}{2}=\)

\(=2^7.10000+500+0,5=1280000+500+0,5=1280500,5\)