Question

So sánh: B= 1/4+1/4^2+1/4^3+...+1/4^1000 và 3/4

Answer 1

\(C=\dfrac{1}{4}+\dfrac{1}{4^2}+...+\dfrac{1}{4^{1000}}\)

\(4C=1+\dfrac{1}{4}+\dfrac{1}{4^2}+...+\dfrac{1}{4^{999}}\)

\(4C-C=3C=1-\dfrac{1}{4^{1000}}\)

\(C=\dfrac{1-\dfrac{1}{4^{1000}}}{3}\)

Vì \(1-\dfrac{1}{4^{1000}}< 1\) nên \(\dfrac{1-\dfrac{1}{4^{1000}}}{3}< \dfrac{1}{3}< \dfrac{3}{4}\)

Vậy \(C=\dfrac{1}{4}+\dfrac{1}{4^2}+...+\dfrac{1}{4^{1000}}< \dfrac{3}{4}\)