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S=\(\left(1+\frac{1}{2}+......+\frac{1}{2002}\right)-2.\left(\frac{1}{2}+\frac{1}{4}+..........+\frac{1}{2002}\right)\)
=\(\left(1+\frac{1}{2}+.........+\frac{1}{2002}\right)-\left(1+\frac{1}{2}+.........+\frac{1}{1001}\right)\)
=\(\frac{1}{1002}+\frac{1}{1003}+...........+\frac{1}{2002}=P\)
\(\Rightarrow S-P=0\)
dat D=1/1x2x3+1/2x3x4+.....+1/1001x1002x1003
2D=2/1x2x3+2/2x3x4+.....+2/1001x1002x1003
2D=1/1x2-1/1002x1003
2D=1/2-1/1005006
2D=502503/1005006-1/1005006
2D=502502/1005006
2D=251251/502503
D=251251/502503:2
D=251251/1005006
Đáp án của tớ là:
\(\frac{1}{1002}+\frac{1}{1003}+...+\frac{1}{2003}=\)\(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2003}\right)-\)\(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1001}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2003}\right)-\)\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2002}\right)-\)\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2002}\right)=\)\(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2003}-\frac{1}{2}-\frac{1}{4}-\frac{1}{6}-...-\frac{1}{2002}\)\(-\frac{1}{2}-\frac{1}{4}-\frac{1}{6}-...-\frac{1}{2002}\)
Vậy:\(1+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2003}=\frac{1}{1002}+\frac{1}{1003}+...+\frac{1}{2003}\)
xin chòa hôm nay mình sẽ giúp bạn lam bài toán này
ta có
1/1002+1/1003+....+1/2003=(1+1/2+1/3+.....+1/2003)-(1+1/2+1/3+....+1/1001)
1/1002+1/1003+....+1/2003=(1+1/2+1/3+.....+1/2003)-(1/2+1/4+1/6+....+1/2002)-(1/2+1/4+1/6+......+1/2002)
1/1002+1/1003+.....+1/2003=1+1/2+1/3+....+1/2003-1/2+1/4+1/6+....+1/2002-1/2-1/4-1/6-....-1/2002
Vậy1/1002+1/1002+.....+1/2003=1-1/2+1/3-1/4+....-2/2002-1/2003
Gọi tổng trên là A, ta có:
a) A = \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2008^2}\) \(< \frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2007.2008}\)
\(< \frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2007}-\frac{1}{2008}\)
\(< \frac{1}{1}-\frac{1}{2008}\)
\(< 1-\frac{1}{2008}\)
Vì 1 - 1/2008 < 1 nên A < 1 - 1/2008 < 1
Vậy \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2008^2}< 1\)
câu b đề sao đấy bạn
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2001}-\frac{1}{2002}\)
\(=\left(1+\frac{1}{3}+...+\frac{1}{2001}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2002}\right)\)
\(=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2002}-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2002}\right)\)
\(=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2002}-1-\frac{1}{2}-...-\frac{1}{1001}\)
\(=\frac{1}{1002}+\frac{1}{1003}+\frac{1}{1004}+...+\frac{1}{2002}\)