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Part 1
Evaluate the following infinite geometric series.
1minusone eleventh
plusStartFraction 1 Over 121 EndFraction
minusStartFraction 1 Over 1331 EndFraction
plustimestimestimes
The sum is
1 + (-1/11) + (1/121) + (-1/1331) + ...
To find the sum of an infinite geometric series, we use the formula:
S = a / (1 - r)
Where:
S = sum of the infinite series
a = first term
r = common ratio
In this case, the first term (a) is 1 and the common ratio (r) is -1/11.
Plugging in the values:
S = 1 / (1 - (-1/11))
S = 1 / (1 + 1/11)
S = 1 / (11/11 + 1/11)
S = 1 / (12/11)
S = 11/12
Therefore, the sum of the infinite geometric series is 11/12.