Compute the following expressions 1 12 14 18 116 132

Compute the following expressions: 1 - 1/2 + 1/4 - 1/8 + 1/16 - ^1/32 + ... - 1/2^13 (and save it into A8.dat); 1/1^0 times 3^2 + 1/3^2 times 5^2 + 1/5^2 times 7^2 + ... with 500 terms (and save it into A9.dat). Recall that 1/5^2 times 7^2 = 1/(25 times 49) = 1/1225

Solution

The series
1 – 1/2 + 1/4 – 1/8 + 1/16... is infinite Geometric Series.

The sum to infinity (S) of any geometric sequence in which the common ratio r is numerically less than 1 is given by

S = a/(1-r) |r| < 1

where
a = first number of the series
r = common ratio

MATLAB CODE:

% define your first 5 n-elements
n = 0 : 4

% generate your sequence
s = (-1).^n ./ 2.^n

% find its sum
s_to_i = sum(s)

OUTPUT:

n =     0     1     2     3     4
s =     1.0000   -0.5000    0.2500   -0.1250    0.0625
s_to_i = 0.6875

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