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).

the answer is 15% decrease

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.