Question

$\frac{1}{1*2*x} + \frac{1}{2*3*x} + \frac{1}{3*4*x} +...+ \frac{1}{15*16*x} =0,3$

Answer 1

1 /x  · (  1 /1·2 + 1 / 2·3 +  ····· + 1 /15 ·16 )  = 0,3 
formula pentru numere consecutive  1 / n · ( n +1 )  = 1 /n -  1 /( n+1 ) 
1/x ·( 1/1 - 1/2    +  1/2   -1/3   +  ······  1/13 -  1/ 14 + 1 /14 -1/15  + 1/15 - 1/16 ) =
= 0,3 
1/x · ( 1/1  -  1 /16 ) =0,3 
15 / 16x  = 0,3
15 = 16· 0,3 ·x 
 x = 15 / 16·0,3  = 15 / 4,8 =25 / 8