MathDB

2017 A4: Sum in Terms of e

Source:

January 29, 2017

2017algebra

Problem Statement

It is well known that the mathematical constant

e

can be written in the form

e = \tfrac{1}{0!}+\tfrac{1}{1!}+\tfrac{1}{2!}+\cdots

. With this in mind, determine the value of

\sum_{j=3}^\infty\dfrac{j}{\lfloor\frac j2\rfloor!}.

Express your answer in terms of

e

.

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