So this one is confusing me:

Question

limit of n as it approaches infinity of (n{SIGMA}i=1) (1/(2^i)

*the n is on top of the sigma notation and i=1 is at the bottom.

I understand that 'i' would equal (n(n+1))/2 however the algebra from there confuses me.

Answer 1

The sum is

1/(2^i)
= 1/2^1 + 1/2^2 + 1/2^3 + ...
= 1/2 + 1/4 + 1/8 + ...

You will recognize that as a geometric series, with

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

Answer 2

so a is the first term in the series and r is the term that is being reused over and over again ?

Answer 3

in the equation a/(1-r)

Answer 4

naturally, since that is the formula for the sum of a G.P.