Write out proof in paragraph form. include contradictions if necessary
5. prove that n(n+1) (2n+1) is always divisible by 6

If , then

which is of course divisible by 6.

Assume the claim holds for . Then if , we have

(I use the distributive property of multiplication to extract the first term, which we've assumed is divisible by 6)

The claim holds for if

is also divisible by 6. With some manipulation we can express this as

which is clearly divisible by 6, so the claim is true for , and this completes the proof (by induction).

x+y = 29, 5x + 2y = 100

step-by-step explanation:

i'm guessing it was a multiple first option was the correct answer

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere