Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = (−3^n)/(4n!)

converges.

Step-by-step explanation:

The convergence analysis of this sequence is done by Ratio Test. That is to say:

, where sequence converges if and only if .

Let be , the ratio for the expression is:

Inasmuch becomes bigger, then . Hence, converges.

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

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