CMR 1/5^2 + 1/6^2 + 1/7^2 + 1/2007^2>1/5
CMR: 1/52+1/62+1/72+...+1/20072 lớn hơn 1/5
\(\frac{1}{5^2}+\frac{1}{6^2}+......+\frac{1}{2007^2}>\frac{1}{5}\)
Có \(\frac{1}{5^2}>\frac{1}{4.5}\)
\(\frac{1}{6^2}>\frac{1}{5.6}\)
\(........\)
\(\frac{1}{2007^2}=\frac{1}{2006.2007}\)
\(\Rightarrow\frac{1}{5^2}+\frac{1}{6^2}+.......+\frac{1}{2007^2}< \frac{1}{4.5}+\frac{1}{5.6}+....+\frac{1}{2006.2007}\)
\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+.....+\frac{1}{2006}-\frac{1}{2007}\)
\(=\frac{1}{4}-\frac{1}{2007}\)
\(=\frac{2003}{8028}>\frac{1}{5}\)
Chứng minh 1/5^2+1/6^2+1/7^2+...+1/2007^2 > 1/5
có thể tham khảo phương pháp giải ở đây https://hoc24.vn/hoi-dap/question/205816.html
Chứng minh rằng : 1/5^2+1/6^2+1/7^2+...+1/2007^2 > 1/5
cầu xin các bạn mở lòng từ bi giúp tớ bài này nhé
chứng minh rằng : 1/5^2 + 1/6^2 + 1/7^2 + ... + 1/2007^2 > 1/5
Chứng minh rằng:
a) \(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2007^2}<\frac{1}{4}\)
b)\(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2007^2}>\frac{1}{5}\)
a) \(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2007^2}<\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{2006\cdot2007}\)
=> \(<\frac{1}{4}-\frac{1}{2007}<\frac{1}{4}\)
\(vậy:\frac{1}{5^2}+\frac{1}{6^2}+...+\frac{1}{2007^2}<\frac{1}{4}\)
b) \(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2007^2}>\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+...+\frac{1}{2007\cdot2008}\)
=> \(>\frac{1}{5}-\frac{1}{2008}>\frac{1}{5}\)
\(vậy:\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2007^2}>\frac{1}{5}\)
Chứng minh : $\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{^{2007^2}}>\frac{1}{5}$
\(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2007^2}>\frac{1}{5}\)
#)Giải :
Ta có : \(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2007^2}>\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{2007.2008}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{2007}-\frac{1}{2008}=\frac{1}{5}-\frac{1}{2008}=\frac{2003}{10004}>\frac{1}{5}\)
\(\Rightarrow\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2007^2}>\frac{1}{5}\)
\(\frac{1}{5}-\frac{1}{2018}>\frac{1}{5}????\)
#)Góp ý :
Chết ! máy tính lỗi rùi :v xin lỗi bn, mk tính nhầm, ph là \(\frac{2003}{10040}>\frac{1}{5}\) nhé @@ sai òi
A=20008+2007/2+2006/3+2005/4+...+2/2007+1/2008 / 1/2+1/3+1/4+1/5+1/6+1/7+...+1/2008
a=...
Câu 15 A= 1/3-3/4+3/5+1/2007-1/36+1/25-2/9
Câu 16 A=1/3- 3/4- (-3/5)+ 1/64- 2/9- 1/36+ 1/15
Câu 17 A=1/2- 2/3+ 3/4- 4/5+ 5/6- 6/7- 5/6+ 4/5- 3/4+ 2/3- 1/2
15: A= 1/3-3/4+3/5+1/2007-1/36+1/15-2/9
Sửa đề:
A=-3/4-2/9-1/36+1/3+3/5+1/15+1/2007
=-27/36-8/36-1/36+5/15+9/15+1/15+1/2007
=-1+1+1/2007=1/2007
16:
\(A=\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}-\dfrac{3}{4}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{64}\)
\(=\dfrac{5+9+1}{15}+\dfrac{-27-8-1}{36}+\dfrac{1}{64}\)
=1/64
17:
=1/2-1/2+2/3-2/3+3/4-3/4+4/5-4/5+5/6-5/6-6/7
=-6/7