How would you sum this?

Question

∞

Σ (1/2)^r

r=0

What does the r mean? Isn't it usually n?

Completely lost, please help, thank you!

Answer 1

you know that (1/2)^r means ;1/2 power r..so if you start to write you will have: 1+ 1/2 + 1/4+...........+1/2^n    

befor solving this you should've known this formula that; 1/2+1/4+..................1/2^n=1-1/2^n   so go back again & write it like me : 1+1-1/2^r=2-1/2^r  cause r here goes to infinitive  so  in 1/2^n the denominator is bcoming bigger so 1/2^n goes to 0.....so the answer would be 2........good luck

Answer 2

∞

Σ (1/2)^r

r=0

its a gp , the sum for an inf gp is :

sum=1/1-a where a is ration of terms

sum=1/1/2 = 2