Question
The sum of the infinite series 2^ 2 2 ! + 2^ 4 4 ! + 2^ 6 6 ! + is equal to
The sum of the infinite series 2^ 2 2 ! + 2^ 4 4 ! + 2^ 6 6 ! + is equal to
C. ( e ^ 2 -1 )^ 2 2 e ^ 2
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
Related: Mathematics — Sequences and Series · All PYQ Banks