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  4. The 15th term of the series 2(1/2)+1(7/13)+1(1/9)+(20/23)+.................. is

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Q. The $15th$ term of the series $2\frac{1}{2}+1\frac{7}{13}+1\frac{1}{9}+\frac{20}{23}+..................$ is

Sequences and Series

Solution:

Reciprocals of the terms of the series are $2/5, 13/20, 9/10, 23/20,...$ or $8/20, 13/20, 18/20, 23/20,....$ Its $nth$ term is
$\frac{8 + ( n-1)5}{20} = \frac{5n+3}{20}$
Therefore, the $15$th term is $\frac{20}{78} = \frac{10}{39}$.