S=1+2*(1/5)+3*(1/5)^2+4(1/5)^3......
If S=a/b, where a and b are coprime positive integers, what is the value of a+b?
To find the value of a + b, we first need to determine the value of S.
The given expression S can be represented as a geometric series with a first term of 1 and a common ratio of 1/5.
We can use the formula for the sum of an infinite geometric series to find the value of S:
S = a / (1 - r)
where a is the first term (1) and r is the common ratio (1/5).
Substituting the values into the formula, we have:
S = 1 / (1 - 1/5)
Simplifying further:
S = 1 / (4/5)
To divide by a fraction, we 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 need to determine the values of a and b separately.
In this case, a = 5 and b = 4.
Finally, we can find the sum of a + b:
a + b = 5 + 4
a + b = 9
So, the value of a + b is 9.