- #1
Benighted
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Homework Statement
Find the limit of the following sequence:
Homework Equations
[itex] \lim_{n \rightarrow + \infty} \sqrt[4] {2n + 1} - \sqrt[4] {n + 1} [/itex]
The Attempt at a Solution
I've tried multiplying the first radical by ## \frac{ \sqrt[4] {2n - 1} } { \sqrt[4] {2n - 1} } ## to make the radical into a square root (and do the analogous thing for the second radical), but that seems to lead nowhere as well as give me an extra denominator to work with.
I've tried multiplying the second radical by 16/16 to get a 2 inside the radical, but that leaves me with ## \sqrt[4] {2n - 2} ##, which isn't much better.
I've tried eyeballing the solution as ##n## approaches infinity; both radicals approach infinity, but ## \infty - \infty ## is indeterminate, and I think I'm supposed to solve it without L'Hospital's rule (it was in my precalculus exercise book before derivatives and L'Hospital's).
I've got about 6 more exercises like this one, with increasingly complex polynomials under radicals.
What am I supposed to do to simplify the exercise? Get both terms under the same radical?
P.S. Sorry if I messed up the limit syntax, this is my first time with LaTeX...