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Numerade Educator

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Problem 8 Easy Difficulty

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

Answer

The first five terms of the given series are
$-\frac{1}{2}, \frac{2}{3},-\frac{3}{7}, \frac{4}{25},-\frac{5}{121}$

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Video Transcript

Kings were going to be working with the factorial. Similar. So let me just write down the relevant factorial values. One factorial is one two Factorial is too three Factorial is three times to which is six for Factorial is four times three times two So four times three factorial four times six is twenty four five. Fact world is five times for factorial one twenty. Okay, so these are the relevant factorial functions that we'll need for figuring out the terms in this sequence. For in equals one, we have minus one to the one. So some negative number negative one over one factorial plus one so minus one half That gives us the first term for an equals to We have minus one squared, so it'LL give us a positive number and then we have to in the numerator two divided by two factorial plus one So two over three, three nickels three We're back to having a negative number minus three over three factorial plus one two minus three over seven chronicles for backto having a positive number. We're just switching off signs here can. That's what this minus one to the end means over here. So four divided by four factorial plus one pour over twenty five. But I really should be putting commas toe separate values in our sequence here and then we just need one more term should be a negative negative five over five factorial plus one the negative five over one twenty one.