Chapter 1: Q24MP (page 1)

Use the series you know to show that:
$l n 3 + \frac{{(l n 3)}^{2}}{2!} + \frac{{(l n 3)}^{3}}{3!} + \dots = 2$

Short Answer

Expert verified

It is shown that the expansion of series $\ln (3) + \frac{\ln {(3)}^{2}}{2!} + \frac{\ln {(3)}^{3}}{3!} + \frac{\ln {(3)}^{4}}{4!} + \dots is 2$

Step by step solution

Maclaurin series and the given series

Series is $\ln (3) + \frac{\ln {(3)}^{2}}{2!} + \frac{\ln {(3)}^{3}}{3!} + \frac{\ln {(3)}^{4}}{4!} + \dots$
The Maclaurin series ofis given below:

$\begin{array}{rcl} e^{x} & = & 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \frac{x^{4}}{4!} + \dots \\ e^{x} - 1 & = & x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \frac{x^{4}}{4!} + \dots \end{array}$

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Use the series you know to show that:
$l n 3 + \frac{{(l n 3)}^{2}}{2!} + \frac{{(l n 3)}^{3}}{3!} + \dots = 2$

Short Answer

Step by step solution

Maclaurin series and the given series

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Use the series you know to show that:ln3+(ln3)22!+(ln3)33!+…=2

Short Answer

Step by step solution

Maclaurin series and the given series

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

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Study anywhere. Anytime. Across all devices.

Use the series you know to show that:
$l n 3 + \frac{{(l n 3)}^{2}}{2!} + \frac{{(l n 3)}^{3}}{3!} + \dots = 2$