Question

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

Answer 1

• On solving these improper fractions into proper fraction and by making numerators be 20.
  

we get series as ,

$=\frac{20}{8}+\frac{20}{13}+\frac{20}{18}+\frac{20}{23}+\frac{20}{28}+......$

Therefore , here denominators are in AP having common difference be $5$.

So , $15th$ term of denominator be = $8+14\times 5=78$

Hence $15th$ term of series will be,

=> $\frac{20}{78}$ = $\frac{10}{39}$