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=\(\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x...x\frac{2013}{2014}x\frac{2014}{2015}\)
=\(\frac{1x2x3x...x2013x2014}{2x3x4x...x2014x2015}\)
=\(\frac{1}{2015}\)
( Dau x la dau nhan)
=\(\frac{3}{2^2}x\frac{8}{3^2}x...x\frac{624}{25^2}\)
=\(\frac{1.3x2.4x...x624}{2^2x3^2x...x25^2}\)
=13/25
\(T=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{575}{576}.\frac{624}{625}\)
\(T=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{23.25}{24.24}.\frac{24.26}{25.25}\)
\(T=\frac{1.2.3....24}{2.3.4...25}.\frac{3.4.5....26}{2.3.4....25}=\frac{1}{25}.\frac{26}{2}=\frac{13}{25}\)
Ta có \(\left(1-\frac{1}{97}\right)\times\left(1-\frac{1}{98}\right)\times.....\times\left(1-\frac{1}{1000}\right).\)
\(=\frac{97-1}{97}\times\frac{98-1}{98}\times.....\times\frac{1000-1}{1000}\)
\(=\frac{96}{97}\times\frac{97}{98}\times....\times\frac{999}{1000}\) (rút gọn hết )
\(=\frac{96}{1000}\)
\(=\frac{12}{125}\)
\(T=(1-\frac{1}{4}).(1-\frac{1}{9}).(1-\frac{1}{16}).....(1-\frac{1}{576}).(1-\frac{1}{625})\)
\(T=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{575}{576}.\frac{624}{625}\)
\(T=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{23.25}{24.24}.\frac{24.26}{25.25}\)
\(T=\frac{1.2.3...23.24}{2.3.4...24.25}.\frac{3.4.5...25.26}{2.3.4...24.25}\)
\(T=\frac{1}{25}.\frac{26}{2}\)
\(T=\frac{1}{25}.13\)
\(T=\frac{13}{25}\)
TK MK NHA
1-1/4-x=8/9-15/16-x-x-575/576-x-624/625=1
= 3/4x8/9x15/16x575/576x624/625=1x3 trên 1x4x2x4 trên3x3x3x5 trên4x4x....23x25trên 24x24x24x26 trên 25x25
=1/1x2/3x3/4x..23/24x24/25=1x2x3x4x...23x24 trên 1x3x4x5...24x25=2/25
3/5x4/3x5/4x6/5x 25/24x26/25=3x4x5x6 x..25x26 trên 5x3x4x5x....24x25=26/5
2/15x26/5=52.50=26/25
Đs 26/25