Problem 2. Let an be the sequence defined by a1 = 1, a2 = 8, and an = an-1 + 2an-2 for n 3. Prove by strong induction that an = 3- 2"- + 2(-1)" for all n > 1. (Hint: You will need to use the inductive hypothesis twice to complete the proof.)

Q: 3y² - 2y-1 (-)-5y²- 2y +6

A:

Q: 5 -100 12 8

A: Solve the given

Q: . 3류 - 2층 : 3% +4/3) 1

A:

Q: 5(18)

A: To find5(18)

Q: 2) 36³x=¹

A:

Q: Expand -5x (2 - 3y)

A: Expand -5x (2 - 3y)

Q: 6.5+ 4

A: To simplify given

Q: 5 1 1 + 2r dr

A:

Q: FIND S + 4 (s² – 8S + 6) -

A:

Q: Expand (x + y) 8.

A: Given: The expression x+y8.

Q: +–3m+–9m+4+5+–10m

A: The expression is given as 1+–3m+–9m+4+5+–10m. Simplifying the given expression. 1+–3m+–9m+4+5+–10m…

Q: 5у 10y

A: Given,    5y/10y    Cancelling y from both numerator and denominator to get,    5/10   Now, 5/10 can…

Q: 4. Expand and simplify (2x + 3)*

A: We have to expand and simplify the following expression: . We will apply the binomial theorem to…

Q: ne binomial:

A:

Q: Expand (a −b)4

A:

Q: d. 1 3a+18 = 1 - 8 a+6

A:

Q: 5 L s² + 2s – 3

A: We know that, Laplace transform of 1/(s-1) = e^t

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

A:

Q: (n + 4)3 =

A: Given query is to expand (n+4)3

Q: (2) 4 2. 2. 2/3

A:

Q: 8 13

A:

Q: 2) Expand the following a) Csa2-2b)

A: I have to exapand (5a^2-2b)

Q: 18(9+7)+3

A: 18(9+7)+3

Q: 8y3 + 216

A:

Q: ydy (1+ у)*

A: We have to find the integral.

Q: Find A.

A: Given

Q: (2 + V-9 )3

A:

Q: 3(m – 5) + m

A: 3(m-5)+m=0 3m-15+m=0 add both side 15 we get 2m=15

Q: 6 1/6 + 6

A:

Q: 8(14-9)+5 32+6

A: The given expression is