1^3+2^3+3^3+...n^3 = [n(n+1)/2]^2

5/2 • 9/10 in simple form

Use the binomial theorem to prove that 2n choose k= 2^n-2k = (2.5)^2n .

(4) For all natural numbers n, 4^n - 1 is a multiple of 3

Arrange the functions √n, 1000 log n, n log n, 2n!, 2n, 3", and Multiple Choice √n, 1000 log n, n log n, 2", 3¹, √n, n² 1000 log n, n log n, √n, 2n!, 2n, 3", 1,000,000 n² 1,000,000 n² 1,000,000 2n! n² 1000 log n, √n, n log n, 1,000,000 1000 log n, n log n, 2n!, 2", 3n 2", 3", 2n! n² 1,000,000 in a list so that each function is big-O of the next function.

Simplify x-1/2(x/5 – x) + (* ¬/5 – 1) (x^/?), -

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

11 (d) 12/13 + (1 1/12 - 11/1/1)

Can someone explain to me each step and why it would be the respective answers?

Prove that n^2+5 >=4n for all integers, n>0.