Question

Fie nemerele:
a=(1 - 1/2) x ( 1-1/3) x (1-1/4) x .... x (1- 1/9)
b =(1+1/2) x (1+1/3) x (1+1/4) x .... x (1+1/8)

Aflati valoarea expresiei 2ab.

Answer 1

calculam parantezele  : 
a =  1 /2  · 2 /3  ·  3 / 4      ....... · 8 / 9 =  simplificam  = 1 / 9 
b  = 3 / 2  · 4 / 3  · 5 / 4 ··········   9 / 8 =  simplificam =  9 / 2 
2ab = 2 ·  1/9    · 9 / 2  = ( 2 · 1 · 9)  / ( 9 · 2) = 18 / 18 =  1