Question

Шексіз кемімелі геометриялық прогрессия  
а) 3+1+3/1+...
ә) 2/1+4/1+8/1+...
б) 8-4+2-...
в) 1-4/3+16/9-...

Answer 1

а) 3  + 1  + 3/1  + ...

q = в2/в1 = 1/3

S = в1/(1-q) = 3/(1-1/3) = 3:2/3 = 9/2 = 4,5

ә) 2/1  + 4/1  + 8/1  + ...

q = в2/в1 = 1/4 : 1/2 = 1/2

S = в1/(1-q) = 1/2 : (1-1/2) = 1/2 : 1/2 = 1

б) 8-4  + 2-...
 = 8  + (-4)  + 2  + ...
 
q = в2/в1 = -4/8 = -1/2

S = в1/(1-q) = 8 : (1   + 1/2) = 8 : 3/2 = 16/3

в) 1-4/3  + 16/9-... = 1  + (-4/3)  + 16/9  + ...

q = в2/в1 = -4/3 :1 = -4/3

S = в1/(1-q) = 1:(1  + 4/3) = 1:7/3 = 3/7