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2 years ago

Please help me!!!!!!!!!!!!!!

Mathematics

1 answer:

OLga [1]2 years ago

3 0

Answer:

d, series and sequence diverge
d, geometric/divergent
c, e (geometric, |r|<1)

Step-by-step explanation:

The sequence terms have a common difference of -5/8. That make it a non-trivial arithmetic sequence, so it diverges.

The series is the sum of terms of the sequence. Any non-trivial arithmetic series diverges.

(A "trivial" arithmetic series has a first term of 0 and a common difference of 0. It is the only kind of <em>arithmetic</em> series that doesn't diverge.)

The terms of the series have a common ratio of -2. That makes it a geometric series. The ratio magnitude is greater than 1, so the series diverges.

A sequence will converge only if the terms have a common difference of 0 or a common ratio with a magnitude less than 1. Of the offered choices, only C and E will converge:

c. geometric, r = 3/5

e. geometric, r = -1/6

_____

<em>Additional comment</em>

The convergence criteria stated for problem 3 applies only to arithmetic and geometric sequences. There are many other kinds of sequences that converge, but these are the kinds being considered in this problem set.

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The graph is attached below

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