Quantrex Academy · Free BITSAT PYQ solutions
BITSAT Mathematics Sequences and Series 2020 BITSAT 2020

BITSAT Mathematics Question (2020) — Solution

Question

The sum of the infinite series 2^ 2 2 ! + 2^ 4 4 ! + 2^ 6 6 ! + is equal to

Options

  1. A. e ^ 2 +1 2 e
  2. B. e ^ 4 +1 2 e ^ 2
  3. C. ( e ^ 2 -1 )^ 2 2 e ^ 2
  4. D. ( e ^ 2 +1 )^ 2 2 e ^ 2

Answer

C. ( e ^ 2 -1 )^ 2 2 e ^ 2

Step-by-step solution

We know that e^ x +e^ -x 2 =1+ x^ 2 2 ! + x^ 4 4 ! + x^ 6 6 ! + keeping x =2, we get Expression = 1 2 [ e^ 2 +e^ -2 2 ]-1= (e^ 2 -1 )^ 2 2 e^ 2

Practice more on Quantrex App →

Related: Mathematics — Sequences and Series · All PYQ Banks