đề 3 :
chứng minh
A = \(\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+.....+\frac{2015}{5^{2015}}< 1\)
TM
Những câu hỏi liên quan
Cho biểu thức sau: \(P=\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}+.....+\frac{2015}{5^{2015}}+\frac{2016}{5^{2016}}\)
Chứng minh 1/4 < P< 1/3
chứng minh \(A=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{4031}{2015^2.2016^2}< 1\)
Cho \(A=\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}+...+\frac{2015}{5^{2015}}\)
CMR a) A<1
b) A<\(\frac{1}{16}\)
CHỨNG MINH RẰNG
\(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+......+\frac{4031}{2015^2.2016^2}< 1\)
A =\(\frac{1}{2!}+\frac{5}{3!}+\frac{11}{4!}+...+\frac{n^2+n-1}{\left(n+1\right)!}\)Chứng minh A < 2 (n \(\in\)N*)Chứng minh B = \(\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+...+\frac{1}{2015!}< 1\)
Xem chi tiết
A =\(\frac{2015+\frac{2014}{2}+\frac{2013}{3}+\frac{2012}{4}+\frac{2011}{5}+.....+\frac{1}{2015}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+......+\frac{1}{2016}}=\)
tìm A
Xét tử: \(2015+\frac{2014}{2}+\frac{2013}{3}+...+\frac{1}{2015}\)
\(=\left(1+1+...+1\right)+\frac{2014}{2}+\frac{2013}{3}+...+\frac{1}{2015}\)( trong ngoặc có 2015 số 1 )
\(=\left(1+\frac{2014}{2}\right)+\left(1+\frac{2013}{3}\right)+...+\left(1+\frac{1}{2015}\right)+1\)
\(=\frac{2016}{2}+\frac{2016}{3}+\frac{2016}{4}+...+\frac{2016}{2015}+\frac{2016}{2016}\)
\(=2016\cdot\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2016}\right)\)
Ghép tử và mẫu \(\frac{2016\cdot\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2016}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2016}}=2016\)
Vậy \(A=2016\)
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Cho N=\(\frac{2}{1}.\frac{4}{3}.\frac{6}{5}...\frac{2016}{2015}\). Chứng minh rằng N<52
Cho \(B=\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{2014}{5^{2015}}\)
Chứng tỏ rằng : B < \(\frac{1}{16}\)
vậy 1/5.2 + 34/3456.23 =vgy0 nên ta có :
1/2.5 + B = 1/16 - B = 32156.097 : 35.98 + -9 -76 , suy ra
B= >89 _980 - -50 + 678 x 54=143.098-2014/5.2015
vậy B=78
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Chua hoc
Hk tot,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
k nhe Nguyen Chau Tuan Kiet
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Chứng minh \(\frac{\sqrt{2}-\sqrt{1}}{3}+\frac{\sqrt{3}-\sqrt{2}}{5}+\frac{\sqrt{4}-\sqrt{3}}{7}+...+\frac{\sqrt{2015}-\sqrt{2014}}{4029}