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How do you use a graphing calculator to find the sum of the geometric series #Sigma 2(1/2)^(n-1)# from n=1 to 15?

1 Answer

Vinícius Ferraz

Jun 5, 2017

#S_{15} =4* (1 - 1/2^15) = 3.99987792968750000000#

Explanation:

#a_0 = 2 ; q = 1/2#

#a_{14} = 2/2^14 = 2^-13#

#S_n = a_0 * frac{1 - q^n}{1-q} = a_0 + a_0 q + ... + a_0 q^{n-1}#

#S_{15} = 2* frac{1 - 0.5^15}{1-0.5}#

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