Find the values of x for which the series converges. (enter your answer using interval notation.) ∞ (x + 9)n n = 1 find the sum of the series for those values of x.

The series will converge when the value of is in the interval .

Step-by-step explanation:

The given series is .

The series is a geometric series and it converges only when the modulus of the term is less than 1.

Here, the term is .

So, the range of convergence of the series will be,

So, the series will converge when the value of is in the interval  .

The convergence of the series will be, (for this range only)

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the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

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