n (3n–1) 2 B. Use mathematical induction to prove that P(n): 1+4+7+..+(3n-2) = n2 1. Use the first 2 values ofn for Basis Step. State your conclusion. for

Q: Use induction to show that Vn EN, 6| 7n – 1.

A: For the solution follow the next step.

Q: 1+ x Σ Aa" (1 – 2)? n=0

A:

Q: Which expression(s) is (are) equivalent to 5 (x+9) + 7 (y + 2) – z? Select ALL that apply. O 5x +…

A: Answer is 4x+7y+59

Q: (2n)! – (2n + 1)! (2n)!

A: It is required to find out , 2n! - 2n+1!2n!  For this we use factorial properties.

Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

Q: 5. Vn EN, Prove the following by mathematical induction. Σ(2n-1)² = n(2n − 1)(2n +1) 3 i=1

A: Let p(n) be the statement,   ∑i=0n(2i-1)2=n(2n-1)(2n+1)3

Q: Prove that: n² + 3n 1 →> 2n² + 1 2 You may use any results from lectures, but you must state them…

A: (.) Given,                We find the limit.

Q: Which simplified choice will result in 200m20n15

A: Consider the following expression…

Q: Find the coefficients of a* in (6 – ½a)6 and kª in (3k – 21)¹2

A: We have to find the coefficients of a4 in 6 - 12a6 and k4 in 3k - 2l12 . Note that,       a - bn…

Q: M² Prove by M I that 1+4+9+ ·· +n³²= £m(n+1)(2n+1)

A: we have to prove that 1+4+9+...+n2=n(n+1)(2n+1)6

Q: Σ –3n \3n 2n+1 in=1

A:

Q: Which of the following is a false statement? In the expansion of (a +b) the coefficient of a b° is…

A: We have to choose the false statement.

Q: Use the Binomial Theorem to expand and simplify the expression. (v- 4)°

A: The binomial theorem is given by a+bn=nc0anb0+nc1an-1b1+...ncna0bn substitute the values…

Q: Prove that 5n²+3n+2 € O(n²).

A:

Q: 7

A:

Q: Find the 7th term of 2+ 2 Write the 5th term of (x + y)1º.

A:

Q: Determine the simplified form of (4 – 37) (–9 + j) – (8 – j5).

A:

Q: Finish this proof by mathematical induction by completing the missing steps 3 and 4 Prove…

A:

Q: Simplification of the boolean expression (A+B+C)(D+E)'+(A+B+C)(D+E) yields which results

A:

Q: use gauss's trick to determine R(n)=2+3+4+...+(n-1)+n+(n+1)

A: It is known that sum of first n numbers is n(n+1)2  that is  1+2+3+----+n=n(n+1)2 Gauss trick method…

Q: (1) Prove by induction: Σ₁(i² − i + 1) = n³+2n

A:

Q: snip

A:

Q: Prove by induction that Vn N 72 n(n+1)(2n - 2) Σ(i²-i) = 6 i=1

A:

Q: How be came? W412 431/ 3 1+ w²+2 0.4w 4-w² = 0, (w² + 2) (4 w²) + 0.4w² = 0, - w4 - 2.4w² - 8 = 0.

A:

Q: hich of the following expressions are equivalent to 2n 4n2 + 4n n+ 5 4n2 + 6n 10 (n+ 1) C 4n (n+1)…

A: given,

Q: Prove the statement by induction .+ (4n – 2) = 2n² 2. 1+ 4 + 7 + . + (3n-2) = n ( 3n - 1) 1. 2 + 6 +…

A:

Q: (5) {1,2} C P({1, 2}).

A: Given  set is {1,2},  we knew that power set of a given set is set of all subsets of the given set.…

Q: (1) Prove by induction: Σ²₁ (i² − i + 1) = n³+2n

A: (1)  Let the given statement is  P n :  ∑i=1n i2 - i + 1 = n3 + 2n3             For  n = 1  we get…

Q: (2) Give a proof by induction of the formula: P(n): 12 +22 + ...+ n² = "(n+ 1)(2n + 1) 6

A:

Q: 2n+2 – 3" Σ - 2. Determine 6n+1 n=0

A: To find: ∑n=0∞2n+2-3n6n+1

Q: How be came? W412 431/ 3 1+ w²+2 0.4w 4-w² = 0, (w² + 2) (4 w²) + 0.4w² = 0, - w4 - 2.4w² - 8 = 0.

A:

Q: Use proof by induction to prove that: =-n°(n+ 1)? %3D r=1

A: Mathemetical Induction

Q: Prove that: n² + 3n 2n² +1 1 2

A: The given problem is to prove the sequence tends to 1/2.Given n2+3n2n2+1.

Q: Give a combinatorial proof of the following identity: 2n (²2) n 2 +n². 2.

A: Prove the following identity.  2nc2=2nc2+n2