# Innequality prove question

• transgalactic
In summary, the conversation is about proving that the remainder, R_5, in the Maclaurin series for sin(x) is negative. The first three terms of the series are x-\frac{x^3}{6}+\frac{x^5}{120}, and the goal is to show that the remaining terms are smaller in absolute value compared to the first three terms.

#### transgalactic

prove that..
$$x-\frac{x^3}{6}+\frac{x^5}{120}>\sin x\\$$
$$R_5=\frac{f^{5}(c)x^5}{5!}$$
i need to prove that the remainder is negative .
$$\sin x=x-\frac{x^3}{6}+\frac{x^5}{120}+R_5$$
$$R_5=\frac{cos(c)x^5}{5!}$$

I'm going to guess that you will use the Maclaurin series for sin(x) and cos(x).

no?/////

i need to show that the remainder is negative??

$$x-\frac{x^3}{6}+\frac{x^5}{120}$$
These are the first three terms of the Maclaurin series for sin(x). Do you know what the terms immediately following them look like? Do you know how successive terms in this Maclaurin series compare in absolute value?

## What is an inequality prove question?

An inequality prove question is a mathematical question that asks for the proof of a statement or inequality. It typically involves using mathematical equations and logic to show that the statement is true or false.

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