Question
Find the sum of the geometric series 1+1/4+1/16+1/64+1/256
Answers
GPT 3.5
To find the sum of the geometric series, we can use the formula for the sum of an infinite geometric series given by:
S = a / (1 - r)
where:
S = sum of the geometric series
a = first term of the series
r = common ratio of the series
In this case, the first term (a) is 1 and the common ratio (r) is 1/4.
S = 1 / (1 - 1/4)
S = 1 / (3/4)
S = 4/3
Therefore, the sum of the geometric series 1 + 1/4 + 1/16 + 1/64 + 1/256 is equal to 4/3.
S = a / (1 - r)
where:
S = sum of the geometric series
a = first term of the series
r = common ratio of the series
In this case, the first term (a) is 1 and the common ratio (r) is 1/4.
S = 1 / (1 - 1/4)
S = 1 / (3/4)
S = 4/3
Therefore, the sum of the geometric series 1 + 1/4 + 1/16 + 1/64 + 1/256 is equal to 4/3.