find Pk + 1 if Pk=2K-1/k!
come on -- just plug in k+1 for k:
Pk+1 = (2(k+1)-1)/(k+1)!
= (2k+1)/(k+1)!
To find Pk + 1, we need to substitute the value of k + 1 into the formula Pk = (2K - 1) / k!.
Let's start with the given formula:
Pk = (2K - 1) / k!
Now, substitute k + 1 for k:
Pk + 1 = (2(K + 1) - 1) / (K + 1)!
Simplifying the numerator:
(2(K + 1) - 1) = 2K + 2 - 1 = 2K + 1
Simplifying the denominator:
(K + 1)! = (K + 1)(K!)
Now substitute the simplified values back into Pk + 1:
Pk + 1 = (2K + 1) / (K + 1)(K!)
So, Pk + 1 is equal to (2K + 1) / (K + 1)(K!).
To find Pk + 1 given that Pk = 2K - 1/k!, we need to substitute (K + 1) for K in the formula.
Step 1: Substitute (K + 1) for K.
Pk + 1 = 2(K + 1) - 1/(K + 1)!
Step 2: Simplify the expression.
Pk + 1 = 2K + 2 - 1/(K + 1)!
Since we cannot further simplify the expression without knowing the value of K, this is the final answer: Pk + 1 = 2K + 2 - 1/(K + 1)!
Note: If you have a specific value for K, you can substitute it into the expression to get the numerical answer.