Prove that the sum of the first n natural numbers is given by this formula: n(n + 1) 1+2 +3 +. .. +n= 2

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A: The given sequence is; {an} = n/(3n-2).

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Q: Find the interval of convergence of (x - 9)" In (4n) n=2 (Use symbolic notation and fractions where ...

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Q: The sequence

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Q: 4. Find the area enclosed by the curve: x=t2 – 2t, y= vt and the y-axis

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) = (1 + x)4 Σ f(x) n = ...

A: Explanation of the answer is as follows

Q: A. For the following primitives, identify the number of essential constants. (x and y are the variab...

A: Topic:- calculus

Q: each

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Q: 5. y( 8x -9y) dx + 2x(x-3y) dy = 0 ans. x'y(2x-3y) = C #5 by another mmethod

A: According to our guideline we can only answer first question and rest can be reposted.

Q: Use the given integral table to find and evaluate the given integral. Given: ∫ 1/√6x - x2 dx

A: Given ∫16x-x2dx To evaluate the integral:

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Q: Kelsey deposited $1,100 at the end of every month into an RRSP for 8 years. The interest rate earned...

A: The accumulated value of the RRSP at the end of 8 years is 127353.74 (rounded to nearest cent)

Q: Solve. Vx+14 =x+2 of Select the correct choice below and, if necessary, fill in the answer box to co...

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Q: Diana invested $1,175 at the end of every month into an investment fund that was earning interest at...

A: This question can be solved using future value of ordinary annuity for the first 8 years and then ap...

Q: 14 n+3 n+2, n=1

A:    ∑n=14n+3n+2Compute the sum of an=n+3n+2 for n=1…4=43+54+65+76=9920

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Q: 1. Consider the relation R1: R2 - R such that (r1, y1)R1 (x2, y2) if and only if both points are on ...

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Q: Let f(x) = 11x^2 (x - 4) + 1. Find the critical points c that correspond to local minima. (Use symbo...

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Q: A point P is moving along the curve y = Vx² + 5. When P reaches the point (2, 3), y is increasing at...

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Q: B. Prove that the given equation is a solution to the given DE: 7. y = Ax + Be* ; (x- 1) y" - xy' + ...

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Q: Use the binomial series to find the Maclaurin series for the function. 4 f(x) = V1 + x 1 f(x) = 1 +-...

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Q: Find all points c satisfying the conclusion of the MVT for the function f(x) = 8x ln(x) + 9 and inte...

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Q: Consider the integral 3e 2 dx . Using u-substitution, what is the appropriate u and du? 2e -2r A u =...

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Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1 + x f(x) = 1 + ±x+ ...

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Q: Determine whether the series converges. k=1

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Q: Evaluate the following limits using L'Hôpital's rule   2. lim x→0+ tanh x/sechx − 1

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Q: sec' 20 tan 20 de

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Q: 1. y = xsin(x + A) 2. y = C,sin3x + C2cos3x + x² – 9 3. y = 3Asinx – 2Bcosx

A: Please see the below picture for detailed solution. 

Q: (x + 1)2 and the line (x+1)?, 1, where a is the same constant. 4. Let Si be the area of the region b...

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Q: Sow) du. #glu)- u+1 Using u-substitution, the integral reduces to a new integral evaluate the new in...

A: Topic:- integration

Q: 2x² + 3x +3 dx (x + 1)

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Q: Differ entiare Y = \og (coc V; ) Ditterentiare り; x& cos cos"s

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Q: Use the graph below to answer the following questions lim f(x) = lim f(x) = x→1* x→4* -4 lim f(x) = ...

A: Follow next step

Q: Solve for the Differential Equation m 1. y= -- 7 2. y = Ce-2* + Cze* + 1 3. Ae* + Be-* = Iny

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Q: Determine whether the alternating series converges. 5ln k k=3 O The series diverges. O The series co...

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Q: Find the slope of the curve y2 + x² = y* – 2x at (-2,1) Find the required derivative by applying the...

A: topic - slope of curve note - As per bartleby guidelines ,we are supposed to answer only first quest...

Q: tan (In 4x) cos (In |(2x)"|)|+C. what is b? The integral of dx is b In A B 2 4 4

A: Given :  ∫tan(ln|4x2|)xdx=bln(|cos(ln|(2x)a|)| +C   To find : Value of b  

Q: 4 8 %3D 4x+ 12 2-9 x-3

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Q: 3. At what points on the urve x = 2 t³, y = 1+ 4t – t² does the tangent line have slope =

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Q: Determine whether the series converges. k=1

A: We use limit test to find convergence or divergence of given series. Follow 2nd step.

Q: dx Given: 7-ge-2x. Using u-substitution and transforming the integrand, find du. A 18e-2xdx B - 18e-...

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Q: Which of the following statements is CORRECT? There is not enough information to determine how many...

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Q: If the limit of x->3- and x->3+ is +♾️, while f(3) is 2, is this a removable or infinite essential d...

A: Given

Q: Find the radius of convergence and the interval of convergence. 00 k(k + 1) k=1 1) First apply the R...

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Q: Let (2) = /2*+1, 4-x, Without graphing, is f(x) continuous at x 2? Clearly justify your answer. x+1,...

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Q: The nutritional content per ounce of three foods is presented in the table below. If a meal consisti...

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