Mixed power relation-1

Mixed power relations-1

It is interesting to note the rhythmic feature in   the following  numeral  relations.

1 + 2²  + 3³  =  32 = 2  x  4²

2 + 3²  + 4³  = 75 =  3 x 5 ²

3 + 4² + 5³ = 144 = 4 x 6¹

4 + 5² + 6³  = 245 = 5 x 7²

5 + 6² + 7³  = 384 = 6 x 8²

 In general it can be written as.

X  + (x+1)²  + (x+2)³ = (x+1) (x+3)²