Use the formula for the binomial series: (1 + x)" = m(m-1)2 + ... + 2! m(m–1).-(m-k+l) ,k + k! 1 + mx + ... 1 + Ek=1' * m(m–1)……(m-k+1) ,k if 1지 < 1 k! 1 to obtain the Maclaurin series for - (1 + x)° (k + 5)! 1 + 6x + > k.! k=2 1 – 6x +E(-1)kk+ 7)' 5! k=2 k! 1 (k + 1 – 6x +E(-1)++5)' k! k=2 (k + 6)! 1+÷) 6! k! 1 – 6x + E(-1y&+1 k + 5)! * k! 1 1— бх + k=2

Q: Find the sum of the series n (r +1) (n+2)* 32 (n +3*) 3/2 as n → 00_ n +(n-1)| 3/2

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Q: Write the first-four terms of approximating In (1.5) using Maclaurin series.

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Q: The sum of the series E 4(5)" is n n=0

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Q: Find the Maclaurin series for the given function. SELECT A) B) sin(10z) (-1)*102m+1,an (2n + 1)! 8…

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Q: Dat

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Q: Vhich is the binomial series for f(): (142)

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Q: (-1)"62n+1 (2n+1)! А. 6 — 3! 63 65 * +...+ +... = 5! 7! В. 1 + (극)2 + (금)3 + (극)4 +…+ (금)" + … = +

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Q: the summation of the two power seriesE=12nc,x"-1 + By writing E=16c,x"+1 = 0, we obtain: in%3D1 2c,…

A: To rewrite the the sum of power series.

Q: f(x) = 2x cos 4n+1 3(2n)! Σ( (-1)^2x n = 0 X

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Q: 3. The power series x- 3 ....... can be expressed as +. 2n+1 8. a. 2n+1 =1 2n-1 b. E(-1)" 2n-1 n=1…

A: The power series is given by x-x33+x55+············ To evaluate : The summation notation of the…

Q: use the biomal series (x + 1)k = 1 + kx + or || < 1 to approximate [¹ k(k − 1) 2! -x² + k(k-1)(k −…

A: Given : x+1k =1 +kx+kk-12!x2+kk-1k-23!x3+......    x&lt;1 To find  :∫01x42+1dx

Q: By shifting the summation index of the following added series +00 +00 En(n-1),x"-4[n(n-1)C₁x"-2 +3 +…

A: Given that ∑n=2∞nn−1Cnxn−4∑n=2∞nn−1Cnxn−2+3∑n=1∞nCnxn+∑n=0∞Cnxn=0. Now, we only need to shift the…

Q: The series 2(- 1)"+1 converges n = 1 Select one: True

A: The given series is ∑n=1∞-1n+1

Q: The binomial series of the form i+3x be written as

A: Binomial Expansion: The binomial expansion for (1+x)n is given by, The given function can be…

Q: Consider the series E (In(2n + 1) – In(2n – 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a,}…

A: Given ∑n=1∞(ln(2n+1)-ln(2n-1))

Q: For matrix A = (4 6 3 5 ). If f(x) = x2 - 5, calculate f(A)?

A: The given matrix is, A=4635. The function is f(x)=x2-5. For matrix multiplication: The number of…

Q: By shifting the summation index of the following added three series n(n-1)C,r* + n(n – 1)C,x*-² -…

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Q: Find a power series for + 3.

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Q: m(m – 1) m(m - 1).(m-k+1) 2 (1+ x) = 1+ ma + x+.. 2! k! to obtain the MacLaurin series for (a)…

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