Solving Inflated Series: Sum of First 20 Terms of a=r^k-1

[member38644]

my problem is regarding sequences:

Sum first 20 terms of a=r^k-1

terms are 2, 4/3, 8/9,...
and ratio is 2/3
and r < 1 so its an inflated series
and 2(2/3)^19 = .009021859795

BUT it is an inflated series right? and my answer is the sum of the
first 20 terms which has to be larger than 2 right? so where am I
going wrong?

 

[TD]

a=r^(k-1) is a formula for the k-th term, not for the sum of the first k terms.
The formula for the sum is: $$s_n=t_{1}\frac{1-q^n}{1-q}$$