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

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.