CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

The question is about Sum of fractions. A sequence in which terms are in fractions is given and we need to find out the sum of the sequence. Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept.

Question 19:What is the sum of \\frac{3}{4}\\) + \\frac{5}{36}\\) + \\frac{7}{144}\\) + \\frac{9}{400}\\) + .... + \\frac{19}{8100}\\) = ?

1. \\frac{9}{10}\\)
2. \\frac{11}{18}\\)
3. \\frac{99}{100}\\)
4. \\frac{80}{81}\\)

Video Explanation

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: How do we go about simplifying this sequence?

\\frac{3}{2^2}\\) + \\frac{5}{6^2}\\) + \\frac{7}{12^2}\\) + \\frac{9}{20^2}\\) ... \\frac{19}{90^2}\\)
So,t_n = \\frac{(2n+1)}{((n)^2(n+1)^2)}\\)
Now, we are back to the partial fractions approach,
t_n = \\frac{(2n+1)}{((n)^2(n+1)^2)}\\) = \\frac{1}{(n)^2}\\) - \\frac{1}{(n+1)^2}\\)
So, the above expression is nothing but
t_n = (\\frac{1}{1^2}\\) - \\frac{1}{2^2}\\)) + (\\frac{1}{2^2}\\) - \\frac{1}{3^2}\\)) + (\\frac{1}{3^2}\\) - \\frac{1}{4^2}\\)) + (\\frac{1}{4^2}\\) - \\frac{1}{5^2}\\)) ... + (\\frac{1}{9^2}\\) - \\frac{1}{10^2}\\)) = (\\frac{1}{1^2}\\) - \\frac{1}{10^2}\\))
= \\frac{99}{100}\\)

The question is "What is the sum of \\frac{3}{4}\\) + \\frac{5}{36}\\) + \\frac{7}{144}\\) + \\frac{9}{400}\\) + .... + \\frac{19}{8100}\\) = ?"

Hence the answer is " \\frac{99}{100}\\)"

Choice C is the correct answer.