Summation of Combination Terms MCQ Quiz in বাংলা - Objective Question with Answer for Summation of Combination Terms - বিনামূল্যে ডাউনলোড করুন [PDF]

Given:

Series is \(\sum^n_1{\frac{1}{(x+3)(x+4)}}\)

Concept Used:

\({\frac{1}{(a)(b)}} = {\frac{1}{(a)}} - {\frac{1}{(b)}}, \space where (a < b)\)

Calculation:

\(\sum^n_1{\frac{1}{(x+3)(x+4)}} = {\frac{1}{(1+3)(1+4)}} + {\frac{1}{(2+3)(2+4)}} + ..........+ {\frac{1}{(n+3)(n+4)}}\)

\(\Rightarrow {\frac{1}{4.5}} + {\frac{1}{5.6}} + ..........+ {\frac{1}{(n+3)(n+4)}}\)

\(\Rightarrow {\frac{1}{4}} - {\frac{1}{5}} + {\frac{1}{5}} - {\frac{1}{6}}..........+ {\frac{1}{(n+3)}} - {\frac{1}{(n+4)}}\)

\(\Rightarrow {\frac{1}{4}} - {\frac{1}{(n+4)}}\)

\(\Rightarrow {\frac{n + 4 - 4}{4.(n+4)}}\)

\(\therefore The \space value \space of \space \sum^n_1{\frac{1}{(x+3)(x+4)}} = {\frac{n}{4.(n+4)}}\)