JEE Main 2022 (Online) 25th June Evening Shift | Sequences and Series Question 106 | Mathematics

If $$\{ {a_i}\} _{i = 1}^n$$, where n is an even integer, is an arithmetic progression with common difference 1, and $$\sum\limits_{i = 1}^n {{a_i} = 192} ,\,\sum\limits_{i = 1}^{n/2} {{a_{2i}} = 120} $$, then n is equal to :

104

JEE Main 2021 (Online) 1st September Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

Let S_n = 1 . (n $$-$$ 1) + 2 . (n $$-$$ 2) + 3 . (n $$-$$ 3) + ..... + (n $$-$$ 1) . 1, n $$\ge$$ 4.

The sum $$\sum\limits_{n = 4}^\infty {\left( {{{2{S_n}} \over {n!}} - {1 \over {(n - 2)!}}} \right)} $$ is equal to :

$${{e - 1} \over 3}$$

$${{e - 2} \over 6}$$

$${e \over 3}$$

$${e \over 6}$$

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