6^(1/2),6^(1/4),6^(1/8)............∞=?

6^(1/2),6^(1/4),6^(1/8)............∞=?

(a)  6                   (b)  ∞

(c)  216               (d)  36

plzz help me in this problem!!!!!

∞=∞

So B.

I assume that we are multiplying these terms together  ???? ......if so......

Notice that this can be written as :

6 ^  [ 1/2 + 1/4 + 1/8 + 1/16.......]

And the sum, S, of this series can be found thusly :

S  =  a / [ 1 - r)    where a is the first term  = 1/2    and r is the common ratio between successive terms = 1/2

So  we have

S = (1/2) / ( 1 - 1/2)  =  (1/2) /(1/2)  = 1

6 ^  [ 1/2 + 1/4 + 1/8 + 1/16.......]   =

6^ [1]  =

6