Prove, by mathematical induction, that for every positive integer , 1 ∙ 2 ∙ 3 + 2 ∙ 3 ∙ 4 + ⋯ + ( + 1)( + 2) = ( + 1)( + 2)( + 3) 4

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

you would need to also lose 1 point for each of the other outcomes for it to be fair.

step-by-step explanation: