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Question

S=1/1.2+1/2.3+1/3.4+1/4.5+...+1/2016.2017

M=2^2/1.2 . 3^2/2.3 . 4^2/3.4...... 99^2/99.100

Answer 1

Câu 1:

S = 1/1.2+1/2.3+1/3.4+1/4.5+ ... 1/2016.2017

S = 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2016-1/2017

S = 1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)- ... +(-1/2016+1/2016)-1/2017

S = 1+0+0+0+...+0-1/2017

S = 1-1/2017

S = 2016/2017

Answer 2

S= 1/1.2+1/2.3+...+1/2016.2017

  = 1/1 - 1/2 + 1/2 - 1/3 + ... + 1/2016 - 1/2017

  = 1 - 1/2017

  = 2016/2017

M= 2^2/1.2.3^2/2.3. ... . 99^2/99.100

   = (2^2.3^2.4^2...99^2)/[(1.3).(2.4).(3.5).... ]
   = (2^2.3^2.4^2...99^2)/(1.2.3^2.4^2.5^2......)

   = (2^2.99^2)/(1.2.99.100) 

   = (2.99)/(1.100) 

   = 99/50