By recognizing the series below as a taylor series evaluated at a particular value of x, find the exact sum of the convergent series. 1 + 3/1! + 9/2! + 27/3! + 81/4! + + 3n/n! +

Step-by-step explanation:

Given is a series as

Recall the expansion of

This expansion is valid for all real values of x.

Comparing this with our series we find that x =3

Hence the given series =

Thus we find that the given series can be recognized with the expansion of exponential series with powers of e and here we see that power of e is 3.

So the given Taylor series is equivalent to

answer: $201

step-by-step explanation: to get the answer, you first get 3 nieces that he sold and multiply it by 67 and get $201, so he earned $201 selling his nieces.

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.