Calculating the Limit of an Infinite Series

Thread starter kayron
Start date May 14, 2011
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Infinite Infinite series Limit Series

AI Thread Summary

The infinite series 2/3! + 4/5! + 6/7! + ... converges to e^-1. To solve such problems, it's helpful to relate the series to known infinite series, particularly those involving the exponential function e. By analyzing the terms of the series, one can identify patterns that align with the series expansion of e or e^-1. This approach simplifies the calculation and leads to the conclusion that the limit of the series is indeed e^-1. Understanding these connections is crucial for tackling similar problems in infinite series.

May 14, 2011

kayron

Homework Statement

2/3!+4/5!+6/7!+...to infinity is equal to?

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May 14, 2011

lewando

Homework Helper

Gold Member

Have you done any problems similar to this? Where are you getting stuck?

May 15, 2011

kayron

yes i have.
the trick is to translate this into an expression of known a known infinite series, like that of e or e^-1
here the answer is e^-1

May 15, 2011

hunt_mat

Homework Helper

Write down e and e^-1, what do you find?

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