Question

Determine whether the following series converges or diverges:

4/n!

Answer 1

\[\sum_{n=1}^{∞}\] \[4/n!\]

Answer 2

it converges to -4+4e

Answer 3

what converges and diverges means?

Answer 4

Converges means that there is a finite and defninite limit that the sum approached, diverges is the opposite

Answer 5

converge is when it gets closer to 0 and diverges is when it gets bigger

Answer 6

converges = the sum stops growing eventually, getting asymptotically closer and closer to a final point.

diverges = as you keep adding more terms the sum just keeps getting bigger and bigger

Answer 7

im confused with the n! factorial i should it remain as n or (n-1)

Answer 8

One must also note that divergence does not necessary mean infinite sums, but it can mean that your sum will fluctuate between different extremes

Answer 9

ohhh okay

Answer 10

Essentially these concepts (divergence and convergence) are defined as limits of a sequence made by the n-th partial sum of a series.