SOLUTION: Find the 9th term of the harmonic sequence 3/2,1/2,3/10,3/14,... n=9

Question 983173: Find the 9th term of the harmonic sequence
3/2,1/2,3/10,3/14,... n=9
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Find the 9th term of the harmonic sequence
,,,,... n=9

Get their reciprocals:

,,,,... n=9

If we write the  with a 3 denominator, as 

we can see the arithmetic sequence which the reciprocals form:

,,,,... n=9

Extend it to 9 terms by adding common ratio  each time:

,,,,,,,,

Reduce all the fraction that will reduce:

,,,,,,,,

Take the reciprocals:

,,,,,,,,

9th term is 

Edwin

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