Let an be the n th digit after the decimal point in 6T + 4e. Evaluate Σα. (1)" an n=1

Q: 4.) Find the value(s) of k such that A is singular. 1 k 2 A = -2 -k 3 1 -4

A: The given matrix is                               A=  1  k    2-2  0 -k   3  1 -4 We have to find…

Q: 19. Let a, = (-1)" Vn 2 1. Calculate the value of an+1 - a, for odd values of n. %3D А. -1 В. -2 С.…

A: As this is a multiple question type, according to Bartleby Answer Rule, only 1st question is to be…

Q: For any n e N, let An = {x € R | –n <x < n}. Prove that NneN An = A1. (Recall that we define 0 ¢ N.)

A:

Q: x2+1 =0 Has soluion in R

A: Solution:

Q: dn-1 for all n E Z with n > 2. Prove that for a 2. Let d = 2, and d, neN, d, =. %3D %3D %3D

A: Mathematical Induction is a special way of proving things. It has only 3 steps: Step 1: Show it is…

Q: Without solving the ODE, determine the Wronskian of two ty" - 2t³y - t³y = 0. solutions to the…

A:

Q: For each n e N, let A, = (}, } + ) %3D Find Unen An. Find Nnen An.

A:

Q: 0 <m < n such that am = e. (Hin

A: Subgroup generated by any element in a finite group will have at most n element where n is order of…

Q: Show that D13 is isomorphic to Inn(D13).

A: Given the Dihedral group D13. We have to check this group is isomorphic to Inn(D13).

Q: (a) an = }(n² + n). (b) an = 2an-1 – an-2 with ao = 0 and aj = 1. (c) an = nan-1 with ao = 1. %3D

A:

Q: 1. Compute P(8), and find the exact values of the six circular functions given that e =- 135°. %3D

A:

Q: Use the error bound to find the smallest value of N for which Error(SN)< 10-9. 1 2ea? dx (Give your…

A: Note that error(SN) represents the error bound of  simpson's rule error bound. We know,

Q: Let a, b eR with a < b. Assume that a + <b - for all n E N. Show that b- = (a, b). %3D n n=1

A: We will show  two sets are equal.

Q: 3 a. Suppose h(n)= 15n° + n and f(n) = 14n°. Is f(n)EN(h(n))? Use the definition of Omega notation.

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Let a, b eR with a < b. Assume that a + <b - for all n e N. Show that n n=1

A:

Q: = x3 + x - rith starting d with the of x after the

A:

Q: The value of x in the second iteration of the equation x3 – 9x + 1 = 0 using Regula Falsi is…

A:

Q: Let a be a constant. Given that 3x In(ax)dr = e18 ( 36 -89 , find In a. 3

A:

Q: 1) Evalúe a) csch (In 3) b) cosh (0)

A:

Q: If E(0) = 0 then is said to be a(n)

A: if Eθ^=θ then θ^ is said to be unbiased estimate for θ.

Q: For all n E N, let An = {0, 2n, 4n, 6n, . . {x € Z|(3n E NU{0})(x = 2n)}. (a) Find (with proof) [U…

A:

Q: Ex : Express the Sum o+ 2+4+6+8 in Sigma nata tion. -2

A:

Q: 14 For: 等,曾 3. 6. 27 3 5 7 5n 6. ... Find the explicit nth term.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: nd all values of z for which zª + 2 – i2/3 = 0 and represent them geometrically. |

A: To solve the given equation by using D'Moivre theorem we find the point. The 4 value of z satisfy…

Q: cos(n") In(4) 1. 1 2. n In(n) n%3D 6n + 3 (-1)" n=1 1 4. n - 5 3.

A:

Q: 23 1 dr Evaluate - Express your answers in the form: Axm + Br" + DxP.

A:

Q: Show that 100 1 arctan(100) – arctan(2) + E s arctan(100) – arctan(2) + 1+ 1002 1+ k2 k=2 1+ 22

A: To show that: arctan100−arctan2+11002≤∑k=210011+k2≤arctan100−arctan2+122

Q: e* sin" x dx, if n id an even integer. -X Evaluate :

A:

Q: Compute V(X) (in GB2) using the shortcut formula. (Enter your answer to four decimal places.)

A: Introduction: A random variable is a variable with an unknown value or a function that gives values…

Q: Q: Prove that : sin' ne -de = na for all n e N. sin' e

A: solution is given below

Q: 9 Find A and A by Hamilt on Hheoren For A=|° E12s -75 -IS

A:

Q: ( Σα - xi-1) = x = x for n > 2. i=2 11 IDDLE: following "proof" th

A: Given that c, x1, x2, ..., xn, y1, y2, ..., yn are 2n+1 given numbers.

Q: Let I be ar. V. has a Binomial dist. B(n,@) with the Pid.f. fex; G)o-0^,X:o,n Show that fex;)…

A: Given that X is a random variable which has binomial distribution Bn,θ with p.d.f is given by:…

Q: 1. For an = 5n2 + 9n3 + 1, an = n2, prove or disprove: rn = O(an) (n → o)?

A: We will use the standard definition.

Q: For xn = 5n² + 9n³ + 1, an = en = n², prove or disprove: an = O(an) (n → 0)?

A:

Q: 4. Show that In sin 6 d0 = – n 2 by applying the mean-value principle to In |1+ z| for |2| <r < 1,…

A: ∫0π2logsin(θ)dθ=12∫0πlogsinθdθ                         =12∫0π2logsin2θdθ…

Q: 482Sim? - созж 2 eqon by roing ē? f(²)= find root of above co newston phasor

A: Newton Raphson method :   Steps : Step-1: Find points a and b such that a&lt;b and…

Q: Suppose P(t)represents the population of a certain mosquito colony, where tt is measured in days.…

A:

Q: Show that for any n E N, n(n + 1)(2n + 1) %3D k=0

A:

Q: 8. Let 2ni S7 = e7 = cos- 27 + isin- 7 7 a. Prove that E¢ = 0 k=0

A: we have ζ7=e2πi7=cos2π7+isin2π7we have to prove…

Q: Let b₁ 2 = sin−¹ (²) and c, = sin-¹ („²7) for all n € N such that n ≥ 2 +00 Σ(1+bn) n=2 Σ(bn-Cn) n=2…

A:

Q: Suppose P(t) represents the population of a certain mosquito colony, where tt is measured in days.…

A: Given p(t) represents the population of a certain mosquito colony Given initial population P(0)=574…

Q: 10.) For n>Liestablish that the in teger nc an't 5) is of the form ok. or n21, establish the in nz1…

A: To establish given relation we will use first principle of mathematical induction. For this we will…

Q: Find the value of c such that enc=14 n=0 Enter an exact value BD

A: Given :∑n=0∞enc=14

Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: Find an expression of for y = 2*ev*, Hint: (a*) = a* . (x) · In a

A: We can find the derivative as below

Q: Suppose P(t) represents the population of a certain mosquito colony, where t is measured in days.…

A: We can find the mosquito population in 17days as below

Q: Let f(n) = 2n – n? + 10n – 7. Show that f(n) is O(n³) using specific values of C and ng-

A: