How do you use a power series to find the exact value of the sum of the series 1+sqrt(2)+2/(2!) +(sqrt(2))^3/(3!) +4/(4!) + ...

Logan Knox

Logan Knox

Answered question

2022-09-23

How do you use a power series to find the exact value of the sum of the series 1 + 2 + 2 2 ! + ( 2 ) 3 3 ! + 4 4 ! +...?

Answer & Explanation

Zariah Fletcher

Zariah Fletcher

Beginner2022-09-24Added 8 answers

Since
1 + x + x 2 2 ! + x 3 3 ! + x 4 4 ! + . . . = e x ,
1 + 2 + ( 2 ) 2 2 ! + ( 2 ) 3 3 ! + ( 2 ) 4 4 ! + . . . = e 2

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