for Define a sequence xn recursively by the rules x1 = 2, x2 = 6, and xn = 3xn-1 – 2xn-2 30, and so on. Use induction to prove that for every n E N, we have | n 2 3. Thus x3 = 14, x4 = - 2n+1 – 2. Xn

Q: Prove by induction that the sun of the first n terms of the sequence 17,20,23,26 is given by the…

A: The given sequence is .The sum of the first  terms of the sequence is .The aim is to prove the sum…

Q: P(X₁ = x₁, ..., Xn = xn) = P(X₁ = x₁) [I²²2 P(X; = Xi| X₁ = X₁, ..., Xi−1 = Xi−1 )

A: Here we have a given equation that

Q: For the sequence -27, – 12, 3, 18, ..., the expression that defines the nth term where a, = -27 is…

A: A sequence is a function from natural number to real numbers. It is denoted by {an} where…

Q: For the sequence an

A: Given, the sequence      an=2(an-1-2), and a1=1

Q: Find the term indicated in the expansion (x + 2y)6; third term.

A: Find the term indicated in the expansion (x + 2y)6; third term.

Q: Find the limit of the sequence 14n2 – 8n – 7 1 18 – n + 7n² . - - - n=1

A:

Q: Find an explicit (non-recursive) formula for the sequence 2an 6an-1 = 0, a1 = 5. %3D -

A:

Q: 10. Find the sum of the coefficients of (2x– 3)°. c. -6560 d. -5120 а. -5660 b. -6780

A:

Q: Write the first, third and fifth terms of the expansion of (3x – 5y)5.

A: Write the first ,third and fifth term of the expansion of (3x-5y)5.

Q: be If all tems except y5 of the sequence Y1, Y2» Y3• '9 given , show that the value of y5 is 56 (y4+…

A:

Q: Use the Geometric Sum identity to prove that, if r 70, then (1 – x)3 1 =1+ (1 - x) + (1 – x)² + |

A: The objectives to use geometry sum identity to prove the following expression.

Q: (d) an 10"+1 +3 x 4"-1+5 is divisible by 9 for all n2 1,

A:

Q: For each integer n>1, let A(n) denote the sum of the integers from 1 to n. For example,…

A:

Q: Find the seventh term of the 10 expansion ( x+ y)º

A: We know that (x+y)n = ∑r=0nCrn xn-r yr Hence (x+y)10 = ∑r=010Cr10 x10-r yr

Q: (4) Suppose that a, b are positive integers such that 6² – 2a² = 1. Prove that there exist positive…

A: It is given that, a and b are positive integers such that:.It has to be proved that there exist…