Chữ nhỏ quá em khó đọc:
\(A=\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}\)
\(3A=1-\dfrac{2}{3^1}+\dfrac{3}{3^2}-\dfrac{4}{3^3}+...+\dfrac{99}{3^{98}}-\dfrac{100}{3^{99}}\)
Cộng vế với vế:
\(4A=1-\dfrac{1}{3^1}+\dfrac{1}{3^2}-\dfrac{1}{3^3}+...+\dfrac{1}{3^{98}}-\dfrac{1}{3^{99}}-\dfrac{100}{3^{100}}\)
\(\Rightarrow\dfrac{4A}{3}=\dfrac{1}{3^1}-\dfrac{1}{3^2}+\dfrac{3}{3^3}-\dfrac{1}{3^4}+...+\dfrac{1}{3^{99}}-\dfrac{1}{3^{100}}-\dfrac{100}{3^{101}}\)
Cộng vế với vế:
\(4A+\dfrac{4A}{3}=1-\dfrac{101}{3^{100}}-\dfrac{100}{3^{101}}< 1\)
\(\Rightarrow\dfrac{16A}{3}< 1\)
\(\Rightarrow A< \dfrac{3}{16}\)
help bài 3 câu a ,b, và c help
