Question

Consider the sequence given by {a1=0, a2m=(a2m-1)/2, a2m+1=1/2+a2m}. Write down an explicit formula for the sequence."

"f(xi ; λ)=(λ^xt exp(-λ))/(x!)"

Answer 1

To write an explicit formula for the given sequence, we can rewrite the given recursive formula and solve for the explicit form. The explicit formula for the sequence is a2m+1 = 1/2 + 2a2m.

Step-by-step explanation:

The given sequence can be written as

a1 = 0

a2m = a2m-1⁄2

a2m+1 = 1⁄2 + a2m

To write an explicit formula for this sequence, we can first rewrite the given recursive formula for a2m+1. Let's start with a2m:

a2m = a2m-1⁄2

Multiplying both sides of this equation by 2, we get:

2a2m = a2m-1

Substitute this equation into the formula for a2m+1, we have:

a2m+1 = 1⁄2 + 2a2m

Therefore, the explicit formula for the sequence is a2m+1 = 1⁄2 + 2a2m