Suppose a1=12−12,a2=23−13,a3=34−14,a4=45−15 ,a5=56−16. a) find an explicit formula for an: . b) determine whether the sequence is convergent or divergent: . (enter "convergent" or "divergent" as appropriate.)

The pattern follows a sequence other than arithmetic and geometric sequence.

(a) The explicit formula

The given parameters are:

Express 4 as 3 + 1

Substitute n for 3

Hence, the explicit formula is:

(b) The sequence type

In (a), we have:

Take LCM

Express -1 as 1 - 2

Split

implies that, the sequence diverges.

Hence, the sequence is a divergent sequence

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I'm going to assume you meant to write fractions (because if are all non-negative integers, the series would clearly diverge), so that

and so on.

a. If the pattern continues as above, we would have the general term

b. Note that we can write as

The series diverges by comparison to the divergent series

hiking down a winding trail.

step-by-step explanation:

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