Chung minh 1/1!+2/3!+3/4!+4/5!+...+99/100!<1
Những câu hỏi liên quan
Cho A= 1/2 . 3/4 . 5/6 . ......... . 99/100
B= 2/3 . 4/5 . ......... . 100/101
Chung minh A<B
chung minh rang 1/3 -1 /3^2 + 3/3^3 -4/3^4+...+99/3^99-100/3^100 < 3/16
chung minh rang 1/3-2/3^2+3/3^3-4/3^4+....+99/3^99-100/3^100<3/16
cho A =1/2*3/4*5/6*...*99/100
B=2/3*4/5*6/7*...*100/101
C=1/2*2/3*4/5*...*98/99
a) so sanh A, B, C
b) Chung minh: A*C< A^2< 1/10
c) Chung minh: 1/15< A< 1/10
Lam giup minh di ai lam duoc minh tich dung cho
chung minh 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16
cho n=1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100 . Chung minh n < 3/16
chung minh rang 1/2!+2/3!+3/4!+....+99/100!<1
chung minh rang : 1 / 2 ^ 2 + 1 / 3 ^ 2 + 1 / 4 ^ 2 + . . . + 1 / 100 ^ 2 < 99 / 100
Hình như sai đề thì phải chứ mk làm ko đc !!!
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A < 1/(1.2) + 1/(2.3) + 1/(3.4) + ...+ 1/(99.100)
<=> A< 1- 1/2 + 1/2 - 1/3 + 1/4 - 1/5 + .. + 1/99 - 1/100
<=> A < 1 - 1/100 < 1 (đpcm)
So với thì đây
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1.Chưng minh rằng (1+/1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh 1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
1.Chưng minh rằng
(1+1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
Xét: (1+1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100) =
(1+1/3+1/5+....+1/99) + (1/2+1/4+1/6+...+1/100) - (1/2+1/4+1/6+...+1/100) x 2 =
(1+1/2+1/3+1/4+1/5+1/6+....+1/99+1/100) - (1/2+1/4+1/6+...+1/100) x 2 =
(1+1/2+1/3+1/4+1/5+1/6+....+1/99+1/100) - (1+1/2+1/3+...+1/50) =
1/51+1/52+1/53+ … + 1/100
Hay:
(1+1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh
1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
Viết lại:
(1+1/3+1/5+ … +1/199) – (1/2+1/4+1/6+ … +1/200) = 1/101+1/102+ … +1/200
Tương tự như trên ta được:
(1+1/2+1/3+1/4+1/5+1/6+....+1/199+1/200) - (1/2+1/4+1/6+...+1/200) x 2 =
(1+1/2+1/3+1/4+1/5+1/6+....+1/199+1/200) - (1+1/2+1/3+...+1/100) =
1/101+1/102+ … +1/200
Hay:
1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
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1 .Chưng minh rằng
(1+1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
Xét: (1+1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100) =
(1+1/3+1/5+....+1/99) + (1/2+1/4+1/6+...+1/100) - (1/2+1/4+1/6+...+1/100) x 2 =
(1+1/2+1/3+1/4+1/5+1/6+....+1/99+1/100) - (1/2+1/4+1/6+...+1/100) x 2 =
(1+1/2+1/3+1/4+1/5+1/6+....+1/99+1/100) - (1+1/2+1/3+...+1/50) =
1/51+1/52+1/53+ … + 1/100
Hay:
(1+1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh
1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
Viết lại:
(1+1/3+1/5+ … +1/199) – (1/2+1/4+1/6+ … +1/200) = 1/101+1/102+ … +1/200
Tương tự như trên ta được:
(1+1/2+1/3+1/4+1/5+1/6+....+1/199+1/200) - (1/2+1/4+1/6+...+1/200) x 2 =
(1+1/2+1/3+1/4+1/5+1/6+....+1/199+1/200) - (1+1/2+1/3+...+1/100) =
1/101+1/102+ … +1/200
Hay:
1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
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1.Chưng minh rằng (1+/1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh 1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
1.Chưng minh rằng (1+/1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh 1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
1.Chưng minh rằng (1+/1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh 1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
1.Chưng minh rằng (1+/1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh 1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
1.Chưng minh rằng (1+/1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh 1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
1.Chưng minh rằng (1+/1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh 1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
1.Chưng minh rằng (1+/1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh 1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
1.Chưng minh rằng (1+/1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh 1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
ai tích mình tích lại
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