By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series. A. 1 + 1/5 + (1/5)^2 + (1/5)^3 + (1/5)^4 ++ (1/5)^n + = .
B. 1 + 5 + 5^2/2! + 5^3/3! + 5^4/4! ++ 5^n/n! += .

The first sum is a geometric series:

Recall that for |x| < 1, we have

Here we have |x| = |1/5| = 1/5 < 1, so the first sum converges to 1/(1 - 1/5) = 5/4.

The second sum is exponential:

Recall that

which converges everywhere, so the second sum converges to exp(5) or e⁵.

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)