CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

CAT Questions | Algebra | Polynomials - Fractions

The question is about Fractions. We need to find out the sum of a series in which each term is a fraction. 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 14: What is the sum of \\frac{1}{1*4}\\) + \\frac{1}{2*5}\\) + \\frac{1}{3*6}\\) + \\frac{1}{4*7}\\) +... ?

  1. \\frac{9}{17}\\)
  2. \\frac{7}{15}\\)
  3. \\frac{11}{18}\\)
  4. \\frac{92}{173}\\)

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Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: How you would simplify it?

={\\frac{1}{3}\\) * [\\frac{1}{1}\\) - \\frac{1}{4}\\) + \\frac{1}{2}\\) - \\frac{1}{5}\\) + \\frac{1}{3}\\) - \\frac{1}{6}\\) + .. \\frac{1}{63}\\) - \\frac{1}{66}\\) + ..]}
As this gives us three decreasing infinite series, we can forget about the final terms. The overall sum is = {\\frac{1}{3}\\) * (\\frac{1}{1}\\) + \\frac{1}{2}\\) + \\frac{1}{3}\\))} = \\frac{1}{3}\\) * \\frac{11}{6}\\) = \\frac{11}{18}\\)

The question is "What is the sum of \\frac{1}{1*4}\\) + \\frac{1}{2*5}\\) + \\frac{1}{3*6}\\) + \\frac{1}{4*7}\\) +... ?"

Hence the answer is "\\frac{11}{18}\\)"

Choice C is the correct answer.


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