JEE Mains · Maths · STD 11 - 8. sequence and series
If \(\sum\limits_{n = 1}^5 {\frac{1}{{n\left( {n + 1} \right)\left( {n + 2} \right)\left( {n + 3} \right)}} = \frac{k}{3}} \) , then \(k\) is equal to
- A \(\frac{1}{6}\)
- B \(\frac{17}{105}\)
- C \(\frac{55}{336}\)
- D \(\frac{19}{112}\)
Answer & Solution
Correct Answer
(C) \(\frac{55}{336}\)
Step-by-step Solution
Detailed explanation
General term of given expression can be written as \({T_r} = \frac{1}{3}\left[ {\frac{1}{{n\left( {n + 1} \right)\left( {n + 2} \right)}} - \frac{1}{{\left( {n + 1} \right)\left( {n + 2} \right)\left( {n + 3} \right)}}} \right]\) on taking summation both the side, we get…
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