to obtain the MacLaurin series for (a) (1+x) 00 (1+x) = 1 + mx + k=0 m(m-1), 21 1-8x+89/2x^2-8-9-10/31x^3+(8*9*10* (b) √1 + x = 1+x/7+(1/7)(-6/7)/21x^2+(1/7)(-6/7)(-13/7)/31x^3 + m(m-1) (m-k+ 1), k! +….. ⠀⠀ + Enter first 4 terms only.
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- (2) find the sum of (6) 1X (2-6) X (2-10²) + 2X (3-4) X( 3_ w0²) + -+ (0-1'x (m-w) x (m-10²); imaginary find the coum of Series 5.247 + 2X 3 w. 2+ 2 1X2 cube root of ority 17 4x5 x₂² x2 + nortonsFind the maclaurin series of 3^xWhat is the 7th term in the Taylor series for f(x) = 5e5* taken about x 7th term = 7-6-5-4-3-2-1-36 - 4?
- Obtain the Taylor series for 1/(1 + x)2 from the series for -1/(1 + x).a. the sequence is given by an=1/(n^7/6) lim n→∞ an= b. the sequence is given by an=(n^2+3n+2)/(4n^2+5n+2) lim n→∞ an= c. the sequence is given by an= (7n^2+2n+4)/8n+8 lim n→∞ an=Obtain the Taylor series for 1/(1 + x) from the series for -1/(1 + x).
- The sum to n terms of a particular series is given by Sn= 17n - 3n^2 (a) Find an expression for the sum to (n–1) terms(b) Find an expression for the n th term of the series (c) Show that the series is an A.P. and find the first term and the common difference.Find a power series representation for x+1/(x+2)Consider the series (z - 9)6 a, = (1 – 9)* + (z- 9)4 3. 2! (1 - 9)* + +... 9- 3! 27 - 4! Find an expression for an an = (x-9)^(2n)M(3^(n)n!) In the summation formula n starts at n = no. What is your starting index ng? (Note that because the validity of either of your answers depends on the other, if you enter only one, both will be marked wrong.)