1.7 Show that 1² +2²+ +n² -1 n(n +1) (2n + 1).

Q: (5) 7(3k – 1)² +26(3k – 1)–8

A: On simplifying the above expression,we get

Q: Show that P(n, 1) + P(n, 2) = (22) – 2 (2), for integers n ≥ 2.

A:

Q: 10. Use the binomial theorem to evaluate (2r³ - y) 5.

A:

Q: 21 divides 4(n+1) + 5(2n-1) whenever n is a positive integer.

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Which simplified choice will result in 200m20n15

A: Consider the following expression…

Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: 3) (n² + 10n+18) ÷ (n+ 5)

A: To divide the following expression.n2+10n+18÷n+5

Q: Show that n² + 4n + 14 is big-Oh (n²)

A: Take k=4 and C=6

Q: Indicate the least integer n such that (3x5 + x²)4 = 0(x¹). E

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: ndicate the least integer n for which (3x5 + x2)4 is O(xn).

A: Solved using the binomial theorem

Q: a) 1 (x-1)(x+2)(x+4)

A:

Q: (Vn)(n2 +n+ 17 is prime)

A: Since, you have posted multiple questions , I am doing the very question (ques 7)  according to our…

Q: (b) Prove that 32n²+1, for n ≥ 1.

A: The given inequality is 3n≥2n2+1, for n≥1. We have to prove this inequality.