Find the sum of the geometric series 4+2+1+...+1/16.

Question

I really need help with this problem

Answer 1

Using just arithmetic:

 

4 + 2 + 1 + 1/2 + 1/4 + 1/8 + 1/16

4 + 2 + 1 + 8/16 + 4/16 + 2/16 + 1/16

7 + 15/16

 

Using the formula:

 

S₇ = 4(1 - 0.5⁷) / (1 - 0.5)

S₇ = 4(1 - 1/128) / 1/2

S₇ = 4(127/128) / 1/2

S₇ = 8(127/128)

S₇ = 127/16

S₇ = 7 15/16

 

 

 

Answer 2

4 is the first term (a), the ratio (r) between all of the terms is (1/2), and the last number of the term can also be represented as 1/16 = ar^(n-1). n being the number of term. We can solve for n to plug into our geometric sum equation. 1/16=(4)(1/2)^(n-1) solving for n gives us that n-1=6 so n=7.

 

The geometric equation is the sum = a[(1-r^n)/(1-r)]

 

sum= 4[(1-.5^7)/(1-.5)] = 7.9375 or 127/16.

 

A really helpful website for further explanation is:

 

http://www.mathsisfun.com/algebra/sequences-sums-geometric.html

 

Hope this helps!