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Answer:
Find the 9th term of the harmonic sequence
3%2F2,1%2F2,3%2F10,3%2F14,... n=9
Get their reciprocals:
Step-by-step explanation:
Find the 9th term of the harmonic sequence
3%2F2,1%2F2,3%2F10,3%2F14,... n=9
Get their reciprocals:
2/3,2/1,10/3,14/3,... n=9
If we write the 2%2F1 with a 3 denominator, as 6/3
we can see the arithmetic sequence which the reciprocals form:
2/3,6/3,10/3,14/3,... n=9
Extend it to 9 terms by adding common ratio 4/3 each time:
2/3,6/3,10/3,14/3,18/3,2/3,2/3,30/3,34/3
Reduce all the fraction that will reduce:
2/3,2/1,10/3,14/3,6/1,22/3,2/3,10/1,34/3
Take the reciprocals:
3/2,1/2,3/10,3/14,1/6,3/22,3/26,1/10,3/34
9th term is 3/34