prove that l+2 +3+.. +h = n(ntl) for n=1,2g3 2 %3D

Q: a) Obtain power series solution in powers of x for (x2 – 1) y" + 3x y' + xy = 0, y(0) = 4, y'(0) = 6

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Q: Use the geometric series formula x5 1 + x = ∞ n=0 1 1 - Y = ∞ Σy" to express the function as a…

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Q: find the sum of these series 1/2+1/6+1/12+1/20+1/30+...+1/2450 use polya's solving technique

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Q: 4. P1,500 payable semi-annually at 6% effective o bn qon

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Q: Find the radius of convergence for: 3" n=D1

A: We have to find the radius of convergence

Q: Find the radius of convergence for: n°x" 3n n=D1

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Q: Find two power series solutions for the followir non-zero terms for each solution. (x² + 2)y" + 3xy'

A: The power series solution of differential equation is solved below

Q: Find the upper darboux sum of f(x)=ln(x) for n equal subintervals on the partition [1,2].

A: The given function is f(x)=ln(x). here, x∈1,2 and P=nn,n+1n,...,n+nn be the partition of [1, 2] in n…

Q: 3 for all n2 1. Then 2" Σ E x, be a series such that 0Sxns Let

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Q: Use 3 (below) with n = 4 to give an improved estimate of the series' sum (better than s4). ur answer…

A: Given: The series are,  sn+∫n+1∞ fxdx ≤ ∑ an ≤ sn +∫n∞fxdx  ......1

Q: What does the nth term test determine for the summation of (e^n)/(e^n+n) from 0 to infinity?

A: We are given the expression,

Q: c) Show that the series Em+2 diverges.

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Q: Derive the power series solution around xo = 0 for the ODE 2x(x + 1)y" + 3(x + 1)y' – y = 0 %3D

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Q: Use linearity to evaluate the sum. 20 j=1

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Q: Find the constant term in the expansion

A: We have to solve the problem

Q: Using Taylor Series, what is the value of y"(0) if y'=x+y2 for y(0)=1?

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Q: 10. It has been lo ponents produced in a certain factory are de hundred is drawn from each day's…

A: A random sample of size one hundred is drawn; n=100 1% of electronic components are defective;…

Q: Apply the power series method. Show the details. y" + y = 0

A: The given differential equation, y''+y=0

Q: 2n2+5 Does the series E- converge or diverge? What happens if I try to use the Ratio Test? Is it…

A: Solve the following

Q: Oe the appropai te test to determine the divagance * (on wer gence the series. 2. कं I

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Q: 01. A gardener was observing thd behavior of the roses that he transplanted a week ago. He observed…

A: ANSWER :

Q: The minimum value of N such that the remainder estimate given in the text guarantees that SN…

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Q: Assuming a series of 5000 values of Y, with Var(Y,) = 81. Suppose that p=(-0.2)K| . Then Var() is…

A: Assuming a series of 5000 values of Y, with Var(Y,) = 81. Given that Px=(-0.2)|k|

Q: Use the Integral Test to determine whether the seriesconverge or diverge. Be sure to check that the…

A: Integral Test: Suppose that f(x) is a continuous, positive and decreasing function on the interval…

Q: xy'=y+x     expand on x =1   (power series)

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Q: 6 By power series method, Solve the following ODES? (2+x)=y ans: y = a. (1 + 1/2 X)

A: A detailed solution is given below

Q: Prove that Ig(n!) = 0(n lg n) (Hint: use Stirling's approximation).

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Q: E (n!)² (K)! Fan what e is convergent ?

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Q: Find the sum of the series as a function of x. x2 + 8 x2 + 8 2) E < 1 6. n=0

A: in geometric series  if common ratio r &lt; 1 then sum where, a = first term  r = common series

Q: Date. Q. Find the Fouries Series f )-- 0 4x <T

A: The given function is: f(x)=-x-π-π&lt;x&lt;0x+π0&lt;x&lt;πWe have to find the Fourier series of the…

Q: It is thought that basketball teams that make too many fouls in a game tend to lose the game even if…

A: We have given that x be the number of fouls more than (i.e., over and above) the opposing team. Let…

Q: n Apply the Integral Test to the series E n=1 n²+1

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Q: The series 1 + vn- 1 + Vna n=1 8

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Q: The series {y} is described by y =5+0.3y,-1 +ɛ + 0.9ɛ-1. Identify the specific ARIMA model. What is…

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Q: Find the values of x for which the series E(-1)". (п + 2)(ӕ — 3)" п(п + 1)5" converges. n=1

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Q: 3" x" radius of conver gent for the series i : (n + 2)(n+ 1) (a)co (b)0

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Q: A 2-person barber shop has 5 chairs to accommodate waiting customers. Poten- tial customers, who…

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Q: A colony of bacteria is grown under ideal conditions in a laboratory so that the population…

A: Given:At the end of 3 hours there are 10,000 bacteria.At the end of 5 hours there are 40,000…

Q: Uses series to solve 2D^2 y + xy + y = 0

A: Please check the equation , there is no first order differential of y,

Q: Find the corresponding area using the attached z-table a) between z=0.25 and z=1.74 b) between…

A: a)P(0.25&lt;Z&lt;1.74)=?=P(Z&lt;1.74)-P(Z&lt;0.25)=0.9591-0.5987=0.3604   z-table :

Q: Use the Integral Test to determine whether the seriesconverge or diverge. Be sure to check that the…

A: Given series is, Draw the curve of given expression,

Q: Find the series solution to 2xy'' – xy' + x (x + 1)y = 0 about x = 0.

A: We are given the differential equation, 2xy'' – xy' + x (x + 1)y = 0 =&gt; x(2y'' – y' + (x + 1)y)=…

Q: G.2 SE25 Apply fimpsen's rule to find the valke of Sdx dividing into A equal parts. 4 -89521

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Q: 7. Use the trapezoid rule with n = 60 to approximate the sum in addition to providing the…

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Q: he radius of convergence 7n E(-1)" (3n)! n=0

A: We have; ∑n=0∞(-1)nx7n(3n)! where an=(-1)nx7n(3n)!

Q: Apply Power Series to find the general solution of t²x' = x – t – 1.

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Q: f(x)= x²/1+x³, power series representation is?

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Q: 1 n³ + nªx²

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