(-1)" Σ Given: sin = x²n+1 for x E R (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact value of the sum n=0

Q: 2. (a) Calculate (i+1)302 + (i − 1)302 and write it in the form of x + iy. (b) Find an upper and…

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Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: Prove & [a+(i-1)d] =na + dn(n-1) where a and d are fixed real numbers. 2 n Use the properties of…

A: To prove :- ∑i=1na+i-1d=na+dnn-12

Q: Simplify the following equation (removing the summation symbols): 2a min(k-1,a) Σ Σ (b-k).…

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Q: Use |S – SN| <bN+1 to find the smallest value of N such that Sy approximates the value of the sum S…

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Q: ba Find f"(x) for the following function: f(x) = (x-4)' Ch Evaluate the following summations: 66 400…

A: Use function property for finding inverse .

Q: 5-A] [CLO 1] Suppose that x, y, z € R. Expand the expression so that it is written without…

A: The expression is given as  (2x+3y+1)(8x-5y+3x+5).

Q: 2.24 Derive the simplest sum-of-products expression for the function f(x₁, x2, x3, x4) X₁ X3 X4 +…

A: we have to derive the simplest sum-of-products expression for the functionFor the given function,…

Q: b) Transform the summation by making the specified change of index variable :k to j using formula…

A: Given summation is: ∑k=17kk+2k-3 The given formula is: j=k-1

Q: Σ (²-2) for j=1 to 50. The summation equals

A: NOTE: Refresh your page if you can't see any equations. .

Q: For each first order ODE, state why or why not the ODE is separable, linear, and/or exact (each one…

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Q: 1] Evaluate (a) -S (s²+1) ² {t sin (b) S 1/2 5² (s² +¹)² (d) S

A: Find Laplace of tsin(t/2)

Q: sinz Calculate Rz-4|<T z(z-R)² dz using Residue Theorem. |z-4|<n z(z-n)²

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Q: Evaluate O x3+4x²+ 6x Select the correct answer below: -1 2² ) ) + 0 O (2 In [x]-In (x² + 4x+6) +…

A: Given thattaking firstly using the partial fraction decompositionon comparing the like terms

Q: Verify that the sequence Un(x) = cos ( (n + n ɛ N form an orthogonal set of functions on [0,1]. That…

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Q: (11) Use the binomial theorem and differentiation to find a formula for the sum i=0 (Hint: Consider…

A: To find: The sum ∑i=0ni-2i-1ni by using the bionomial theorem and differentiation.

Q: Use |S – SN| < bN+1 to find the smallest value of N such that Sy approximates the value of the sum S…

A: Here, we have S=∑n=1∞(-1)n+1n(n+1)(n+2). So, the n th term is an=(-1)n+1n(n+1)(n+2)…

Q: Evaluate: L || e" 3t cos 2τdτ 4 s-3 s [(s – 3)² + 4] s[(s – 3) + 4] | s-3 1 (s – 3)² + 4 (s – 3)' +…

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Q: Express In (2) in the form a + ib. (Simplify your answer completely.) In(z) = BRITK In( 4√2 ) + 1 (…

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Q: Find the lower sum for f(x)=x2 over [−1,1] with n=4. Give your answer in fractional form.

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Q: Σ(n+1)an+1€* + * Σ 2ana" = 0, then at = 20m n=0 Q5. If (a) 0 n (b) +30 αφ 2 απ do 00 8

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Q: Use |S – SN| < bN+1 to find the smallest value of N such that SN approximates the value of the sum S…

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Q: Compute the double sum E-1 E=1 i²/(5 + ') .

A: To solve the double summations, the first step is to isolate the summation that is ∑ present on the…

Q: Use |S – SN| < bN +1 to find the smallest value of N such that Sy approximates the value of the sum…

A: According to the given information, it is required to find the smallest value of N such that SN…

Q: (i) Derive the continued fraction of v7. (ii) Find the value of ß, given its continued fraction…

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Q: 2. (a) Show that k!n-k-1 = for n>0 and ka nonnegative integer. 5. e-nxxk dx

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Q: 30 (a) Find the sum of 2k+1. k=2 (b) Show that if Re z < 0, then Je| <1 and find the sum of ) ek*.…

A: i have given the formulas that i have used in the step where i have used them

Q: (a) Write using summation notation: 1 +1 + 1 + 32 + 1 3n (b) Transform the summation by making the…

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Q: If I = may be Evaluate I 20 do 1-2p000 + p² written using show that it 3=eja dz (1-P3)(3-P) of the…

A: Let the given integral is  --------- (1)            For evaluate the above integral consider the…

Q: 1. What is the formula for the following sum Σ" (r + 1)(r + 5) =1 2. Using your formula from…

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Q: 2. [(x – 1) + 5][(x – 1) – 51]. Write the answer in the standard form

A: To write in standard form.

Q: If esc() + + k = cot 3-2√3 3 0-√3 1 √3 O- 3-6 3 4T 3 then the exact value of k is

A: csc(π3)+k=cot(4π3)we know   cscx=1sinxtanx=1cotx

Q: Say that the function f(x) is x for -π < x < 0 and zero for 0 < x < π. Find the a0 coefficient for…

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Q: 4(-1)" Σ 3) Estimate 2N 1 correct to one decimal place. N-1

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