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Ta có :
S = 1 21 + 1 22 + 1 23 + ⋯ + 1 29 + 1 30 > 1 30 + ⋯ 1 30 = 10 30 = 1 3 .
Vậy S > 1 3
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(\(\frac{121}{122}\). \(\frac{123}{125}\)) .(\(\frac{1995}{1996}\).\(\frac{17}{16}\)- \(\frac{21}{25}\):\(\frac{16}{17}\)).(\(\frac{42}{30}\).\(\frac{75}{23}\)-\(\frac{19}{23}\).\(\frac{210}{38}\))
= (121/122 . 123/125) . ( 1995/1996 . 17/16 - 21/25 : 16/ 17) . 0
= 0
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a) 1313/2121 . 165165/143143 . 424242/151515
= 13/21 . 15/13 . 14/5
= 2
Ps: Rút gọn tới tối giản r tính dễ hơn ế. ;)
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= (-123) x (-25) - 123 x 89 + 123 x 89 - 123 x 125
= 123 x 25 - 123 x 89 + 123 x 89 - 123 x 125
= 123 x (25 - 125) - (123 x 89 - 123 x 89)
= 123 x (-100) - 0
= -12 300
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1 - 1/2 + 1/3 - 1/4 + .. + 1/121 - 1/122 + 1/123
= ( 1 + 1/3 + ... + 1/121 + 1/123 ) - ( 1/2 + 1/4 + .. + 1/122 )
Đến bước này ta sẽ cùng cộng 2 vế với : 1/2 + 1/4 + .. + 1/122
= ( 1 + 1/2 + 1/3 + 1/4 + ...+ 1/121 + 1/122 + 1/123 ) - 2. ( 1/2 + 1/4 + .. + 1/122 )
= ( 1 + 1/2 + 1/3 + ...+ 1/122 +1 /123 ) - ( 1 + 1/2 + ...+ 1/61 )
= 1/62 + 1/63 + ..+1/122 + 1/123
Chúc học giỏi !!
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25+123+122-129+1234
=32+123+144-129+1234
=155+144-129+1234
=299-129+1234
=170+1234
=1404
2^5+123+12^2-129+1234=
=(32+123)+(144-129)+1234
=155+15+1234=1404