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Numerade Educator

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Problem 4 Easy Difficulty

.List the first five terms of the sequence.
$ a_n = \frac {n^2 - 1}{n^2 + 1} $

Answer

First five terms are : $0, \frac{3}{5}, \frac{4}{5}, \frac{15}{17}, \frac{12}{13}$

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Video Transcript

for in equals one, we have one squared, minus one over one squared, plus one. So we have zero over two, which is just zero. That's the first terminar sequence for in equals to we have two squared, which is four minus one over four. Plus one of three over five for n equals three, three squared, minus one over three squared, plus one. So that's nine minutes. Watches. Eight over nine plus watches. Ten. And this simplifies to four fifths. Yeah, you're in equals four. We have four squared, which is sixteen minus one, divided by sixteen plus one. So fifteen over seventeen and then for in equals five. This will give us the fifth term. In our sequence. We have five squared, minus one over five squared, plus one. So twenty four over twenty six, which simplifies to twelve over thirteen. Okay, so here is the first time three fifty is the next term. Four fifty is the next time. Fifteen over seventeen is the next term. Twelve over thirteen is the next term. And that gives us the first five times