Question

Question 21 1 pts Recall the power series expansion 1 = 1 - x + x2 – 23 + ... on the interval (-1, 1). Use the given expansion to derive a power series expansion for 1772 Show at least 3 non-zero terms. • 1-x2 + x4 - x +... 0 - 1 + x2-x4 + x + ... 1 + x2 + x4 + x + ... 1+x+x2 + x3 + ... 0-1 + x - x2 + x3 - ...

I just need 23, I have 21 and 22, but since it is a parts question this is context. Thank you!

Answer 1

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Solution:-

Elox + x2 – 213+ --- ; X6 (411) Itx to jes Power series expansion of I Ital HC (-1,1) =) *? E (alill replace a by a? in es" in, we we get = ! -? + 24-26 Itna --- Opticom © to using en Sitmax - siv - x2 +344 -36 + ) da JA- 14 - 2% + - Moodne I Hero, thadumuy variable

23 A tot ce = 31.62 + since, this is an alternating series, so by the Alternating Series estimation theorm, which says (1) : ( The series must be decreasing an samas (gt is true, as Inici) limit of the series must be re lim bn col true as Inici) then, we can calculate the essor Rul = 15-501 Sbati (Magno of terms taken from series expansion) at x = 0.1, A₂= ((0.1)) = 2x100 = 0.000002 of x = 0.1, 04: 110:1)2) = 1.4 3x16° < 0.000001 to, we need to consider 3 terms, ten" (01) - 01- (01+ (0135 = 0.0996686662

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