\(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)...\left(1-\frac{1}{13^2}\right)\) ai chỉ mình với, thanks
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(1-1/3).(1-1/5).(1-1/7).(1-1/9).(1-1/11).(1-1/13).(1-1/2).(1-1/4).(1-1/6).(1-1/8).(1-1/10)
=2/3.4/5.6/7.8/9.10/11.12/13.1/2.3/4.5/6.7/8.9/10
=8/15.48/63.120/143.3/8.35/48.9/10
=384/945.360/1144.315/480
=138240/1081080.315/480
=43545600/518918400=84/1001
\(=-\left(1-\frac{1}{2^2}\right).\left(1-\frac{1}{3^2}\right)...\left(1-\frac{1}{100^2}\right)\)
\(=-\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}...\frac{100^2-1}{100^2}\)
\(=-\frac{1.3}{2^2}.\frac{2.4}{3^2}.....\frac{99.101}{100^2}\)
\(=-\frac{1.2....99}{2.3...100}.\frac{3.4....101}{2.3...100}\)
\(=-\frac{1}{100}.\frac{101}{2}=\frac{-101}{200}\)
Học good
\(=-\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)...\left(1-\frac{1}{100^2}\right)\)
\(=-\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}...\frac{100^2-1}{100^2}\)
\(=-\frac{1.3}{2^2}\cdot\frac{2.4}{3^2}...\frac{99.101}{100^2}\)
\(=-\frac{1.2...99}{2.3...100}\cdot\frac{3.4...101}{2.3.100}\)
\(=-\frac{1}{100}\cdot\frac{101}{2}\)
\(=-\frac{101}{200}\)
\(Taco\):
\(A=\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right).......................\left(1-\frac{1}{1+2+3+.............+2018}\right)\)
\(A=\left(\frac{1+2}{1+2}-\frac{1}{1+2}\right).............\left(\frac{1+2+3+......+2018}{1+2+3+.......+2018}-\frac{1}{1+2+3+......+2018}\right)\)
\(A=\left(\frac{2}{1+2}\right)...........\left(\frac{2+3+.......+2018}{1+2+3+......+2018}\right)\)
\(\Rightarrow A+2017.\left(\frac{1}{3}\right).....\frac{2+3+.....+2018}{1+2+3+...+2018}=1.1.1......1=1\)
\(.................................\)
a)
1/4:(31/16-2+1/2)+1
=1/4:(-1/16+1/2)+1
=(1/4:7/16)+1
=4/7+1
=11/7
b)
43/6:(-7/6)+65/6.(-7/6)+1/2
=-43/7+-455/36+1/2
=-4607/252
c)
1/4+11/2.5/2+-2
=23/4.5/2+-2
=115/8+-2
=99/8
d) bài 4 rất dễ bạn tự làm đi nhé
tick cho mk đi nhanh lên đó nhiên
=
(1 - 1/22).(1 - 1/32).(1 - 1/42)...(1 - 1/132)
= 3/4 . 8/9 . 15/16 ... 168/169
= 1.3/2.2 . 2.4/3.3 . 3.5/4.4 ... 12.14/13.13
= 1.2.3...12/2.3.4...13 . 3.4.5...14/2.3.4...13
= 1/13 . 14/2
= 1/13 . 7
= 7/13
Cái này lp 6, ko phải lp 8 nha bn
Ủng hộ mk nha ☆_☆^_-