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

Question

The 15th term of the series 2(1/2)+1(7/13)+1(1/9)+(20/23)+.................. is (A) (10/39) (B) (10/2) (C) (10/23) (D) none of these

Tardigrade Admin · Accepted Answer

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 (8 + ( n-1)5/20) = (5n+3/20) Therefore, the 15th term is (20/78) = (10/39).

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

$\frac{10}{39}$

$\frac{10}{2}$

$\frac{10}{23}$

none of these

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 $n t h$ term is
$\frac{8 + ( n - 1 ) 5}{20} = \frac{5 n + 3}{20}$
Therefore, the $15$ th term is $\frac{20}{78} = \frac{10}{39}$ .

Q. The 15th term of the series 221​+1137​+191​+2320​+.................. is

3910​

210​

2310​