CHỨNG MINH RẰNG:
A = \(\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{11}{5^{12}}< \frac{1}{16}\)
cho biểu thức A= \(\frac{1}{5^2}\)+\(\frac{2}{5^3}\)+\(\frac{3}{5^4}\)+.....+\(\frac{n}{5^{n+1}}\)+...+\(\frac{11}{5^{12}}\)với n thuộc N
chứng minh rằng:A<\(\frac{1}{16}\)
Chứng minh: \(\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{11}{5^{12}}<\frac{1}{16}\)
\(\left(\frac{1}{5^2}+\frac{2}{5^3}+.....+\frac{11}{5^{12}}\right)\)
=\(\left(\frac{1}{5^2}+\frac{2}{5^3}+.....+\frac{11}{5^{12}}\right)\)<\(\frac{1}{4.5}+\frac{2}{4.5.6}+...+\frac{11}{4.5.6...15}\)
=???
Chứng minh:
\(\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{11}{5^{12}}<\frac{1}{16}\)
Cho \(A=\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{n}{5^{n+1}}+...+\frac{11}{5^{12}}\)
Chứng minh A<\(\frac{1}{16}\)
Cho A=\(\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{n}{5^{n+1}}+...+\frac{11}{5^{12}}\)với n\(\inℕ\).Chứng minh rằng A<\(\frac{1}{16}\)
Giúp mình với, hiện đang cần gấp lắm.
5A=\(\frac{1}{5}+\frac{2}{5^2}...+\frac{n}{5^n}...+\frac{11}{5^{11}}\)
=>4A=5A-A=\(\frac{1}{5}+\frac{1}{5^2}...+\frac{1}{5^{11}}-\frac{11}{5^{12}}\)
=>20A=\(1+\frac{1}{5}+...+\frac{1}{5^{10}}-\frac{11}{5^{11}}\)
=>16A=20A-4A=\(1-\frac{1}{5^{11}}+\frac{11}{5^{12}}-\frac{11}{5^{11}}\)
Mà \(1-\frac{1}{5^{11}}< 1\),\(\frac{11}{5^{12}}-\frac{11}{5^{11}}< 0\)
=>16A<1
Do đó: A<1/16(đpcm)
Cho A = \(\frac{1}{5^2}+\frac{1}{5^3}+\frac{1}{5^4}+.......+\frac{n}{5^{n+1}}+.......+\frac{11}{5^{12}}\) với n \(\in\) N. Chứng minh rằng A < \(\frac{1}{16}\)
Giúp mk vs
Cho \(A=\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{n}{5^{n+1}}+...+\frac{11}{5^{12}}\)với \(n\in N.\)Chứng minh rằng \(A<\frac{1}{16}\)
\(A=\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{n}{5^{n+1}}+\frac{11}{5^{12}}\)với \(n\in N.\) Chứng minh rằng \(A<\frac{1}{16}\)
Cho A =\(\frac{1}{^{5^2}}\)+\(\frac{2}{5^3}\)+\(\frac{3}{5^4}\)+...+\(\frac{n}{5^{n+1}}\)+...+\(\frac{11}{5^{12}}\)với n thuộc N chứng minh rằng A<\(\frac{1}{16}\)