an || n! 5n 4

Q: 4. Conclude that n2 n=1 ||

A:

Q: 'Disprove the statement: For any n E N, if n² +3 is prime, then 2n+7 is prime.

A:

Q: Use induction to show that n4 + 15 is a multiple of 16 for every positive odd integer n.

A:

Q: Find the value of  n! (n − r)!r!  when n = 6 and r = 4.

A:

Q: If then A 1 = A = || = [6 0 0 030 0 7 2

A: Given is the matrix .The objective is to determine its inverse.

Q: 2. Evaluate f]x-1dx 1 O 2 O None of these

A:

Q: For every integer n > 0, 1+2+22 + · + 2" = 2"+1 – 1.

A: Given: The statement 1+2+22+⋯+2n=2n+1-1 Proof: Base step: Show the statement is true when n=0.…

Q: If a, = n(a, -1) and a, = 1, what is the value of (1) 5 (3) 120 (2) 20 (4) 720

A: Here we have,

Q: (10)5n n! 17 Select one: True False

A: Find true or false

Q: If n∈Z, then 4|n2 or 4|(n2−1).

A: First, we need to understand the problem. The question is asking whether for any integer n, either…

Q: - Show that an = is monotone. n+2n+7 "}= •

A:

Q: (b) 6 + 7 + 8 + 9 + ... + k

A: (b) Given that 6+7+8+9+...+k The objective is to find the sum. The formula for sum of numbers are,…

Q: Evaluate Jx√x²+7dx ○ (x+7) +C 3 ○ (x²+7)³¹² + C O +7x+ C O 3(x+7) +

A:

Q: . Use mathematical induction to show that n Σ r=1 (2r − 1)² = 1² + 3² +5² + + (2n − 1)² = = n(2n −…

A:

Q: 2|x−2|+6<0

A: Subtract 6 from both sides. Then divide by 2.

Q: Prove that if 10|n, then 10|n^2+n

A: Prove that if 10|n, then 10|n^2+n