# AP Calculus 1.1 Sequences and Series

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AP Calculus 1.1 Sequences and Series. Find the Maclaurin series for the equation.

AP Calculus | Sequences and Series |

MPAC 5 | Building notational fluency |

### Transcript

a mess All right first of all what the heck

is the maclaurin series No not exactly Well in calculus

the maclaurin series is the expansion of a function that

revolves around x equals zero So this is the formula

f zero plus f prime of zero x plus f

double prime of zero over to factorial times x squared

et cetera You get our drift here see the pattern

We could make a tail and calculate the derivatives evaluated

at zero to find the maclaurin series of function given

But that would take some time And we're busy people

We've got laundry to do a much more efficient ways

to notice that x squared over one plus x equals

x squared times one over one minus negative x Well

we also know where we should know that The maclaurin

series for one over one minus acts is the summation

Of x to the power from any equal zero to

infinity so substituting the negative acts into the summation notation

and multiplying it by x squared we get x squared

times The summation of negative x to the power from

n equals zero to infinity still doesn't look like any

of our answer choices so let's simplify it even more

We can pull a negative one to the end out

of the negative expedient and we can combine the x

squared to the x to the end with the first

basic exponents room Whenever you multiply to terms with the

same base you can add the exponents Remember that Well

we're left with negative one to the end and x

to the power of end plus too so we're going

with answer joyce b o sounds like our laundry's done 00:02:03.879 --> [endTime] well we'll get it tomorrow Oh