S=1 + 2(1/5) + 3(1/5)^2 + 4(1/5)^3 +5(1/5)^4…...........infinite......... If
s=a/b
,
where a and
b are coprime positive integers, what is the
value of a+b?
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I get 25/16 so a+b=41
How far do you get?
To find the value of S, we can use the concept of an infinite geometric series.
An infinite series in the form of a geometric series has a common ratio between each term. In this case, the common ratio is (1/5).
The sum of an infinite geometric series can be calculated using the formula:
S = a / (1 - r)
where "a" is the first term and "r" is the common ratio.
In the given series, the first term "a" is 1. The common ratio "r" is (1/5).
S = 1 / (1 - 1/5)
Simplifying the expression:
S = 1 / (4/5)
To divide by a fraction, we can multiply by its reciprocal:
S = 1 * (5/4)
S = 5/4
Therefore, S is equal to 5/4.
To find the value of a+b, we add the numerator and denominator of the fraction:
a + b = 5 + 4
a + b = 9
Hence, the value of a+b is 9.