Question

bài 1:tìm X

phần a, 1/1x2 + 1/ 2x 3 + 1/ 3 x4 + ....+ 1/ X x( X +1)= 499 / 500

phần b,1/1x3 + 1/3x5 + 1/ 5 x 7+ ....+ 1/X x ( X + 2 )= 20 /41

 

Answer 1

a) 1/1.2 + 1/2.3 + 1/3.4 + .... + 1/x.(x+1) = 499/500

1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/x - 1/x+1 = 499/500

1 - 1/x+1 = 499/500

1/x+1 = 1 - 499/500

1/x+1 = 1/500

x + 1 = 500

     x = 500 - 1 

     x = 499

b) 1/1.3 + 1/3.5 + 1/5.7 + .... + 1/x.(x+2) = 20/41

1/2 . [ 2/1.3 + 2/3.5 + 2/5.7 + ... + 2/x.(x+2) ] = 20/41

1/2 . [ 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/x - 1/x+2 ] = 20/41

1/2 . [ 1 - 1/x+2 ) = 20/41

1 - 1/x+2 = 20/41 : 1/2

1 - 1/x+2 = 40/41

1/x+2 = 1 - 40/41

1/x+2 = 1/41

x + 2 = 41

      x = 41 - 2 

      x = 39