SOLUTION: Harmonic sequence: 2,2/3,2/5,2/7 with solution What is the next term in the harmonic sequence 1/11,1/15,1/19,1/23,...? With solution What is the nth term of the harmonic s

Harmonic sequence:

2,2/3,2/5,2/7 with solution 

A harmonic sequence is the sequence of reciprocals of the terms of
an arithmetic sequence.

So we make the corresponding arithmetic sequence by taking reciprocals
of the terms:

1/2, 3/2, 5/2, 7/2, which has a1 = 1/2, and d = 2/2 or 1

If has nth term an=a1+(n-1)d
                an=1/2+(n-1)(1)
                an=1/2+n-1
                an=n-1/2
                an=2n/n-1/n
                an=(2n-1)/n

So the nth term of the original harmonic sequence is the reciprocal of that:

                an=n/(2n-1)

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For the others, form the corresponding arithmetic sequence, and proceed as 
above.

Edwin