Let (an) be a sequence of positive real numbers 1 2 such that lim - a Then lim a, 4 is equal 84-8 to.?

Question

Let (an) be a sequence of positive real numbers 1 2 such that lim - a Then lim  a, 4 is equal 84-8 to.?

Answer

The given sequence:

Let (an) be a sequence of positive real numbers such that:

lim_n→∞ -a_n = -8

Finding the limit:

We are asked to find the value of:

lim_n→∞ a_n + 4

Since the limit of -a_n is -8, we can rewrite it as:

lim_n→∞ (-a_n) = -8

Using the properties of limits:

We know that if lim_n→∞ f(n) = L, then lim_n→∞ (-f(n)) = -L.

Using this property, we can rewrite the given limit as:

lim_n→∞ (-a_n) = -(-8) = 8

Applying limit rules:

Next, we can use the property that if lim_n→∞ f(n) = L, then lim_n→∞ [f(n) + c] = L + c, where c is a constant.

Applying this property to our limit, we have:

lim_n→∞ [(-a_n) + 4] = 8 + 4 = 12

Final result:

Therefore, the value of lim_n→∞ a_n + 4 is equal to 12.

In summary: