Confusion.....Help....

why lim (n---->∞) 0 * n = 0.....
even when we know that 0 * ∞ is an indeterminate quantity......

plzzz xplain.....(sorry don't know how to write this in latex)

thanks in advance....

#HelpMe! #Advice #MathProblem #Math #Opinions

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Comments

Do you mean 0^∞ or 0 x ∞ ?

Bhargav Das - 8 years, 1 month ago

0 * ∞

A Former Brilliant Member - 8 years, 1 month ago

$\lim_{n \to +\infty} 0*n$

Aditya Parson - 8 years, 1 month ago

Because $\infty \cdot 0$ is indeterminate, we need to be able to simplify it in the limit. It simplifies to ${lim}_{n \rightarrow +\infty } 0$ which is of course zero. The whole idea of a limit is to sort of express an indeterminate quantity. So as n gets very large, zero times n is still zero. That's all that's saying.

Bob Krueger - 8 years, 1 month ago

thanks....guys...u cleared my this confusion...:)

A Former Brilliant Member - 8 years, 1 month ago

Agreeing with Bob K. Before applying the limit we need to get rid of indeterminate form hence $0 \cdot n$ gives $0$ . Another way to think about is that limits with $n \rightarrow \infty$ is limit of this sequence $0 \cdot n_1+0 \cdot n_2 \ldots$ in this case. Obviously with each term zero, limit is also zero.

Nishanth Hegde - 8 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$