Question

Pattern question i guess ? I need part c) working please thankiew :))

Answer 1

From "Series 1" we know, that:


`1+2+3+\ldots+n=(n(n+1))/(2)`

and from "Series 2":


`1^3+2^3+3^3+\ldots+n^3=(1+2+3+\ldots+n)^2`

c)


`3^3+6^3+9^3+\ldots+30^3=(1\cdot3)^3+(2\cdot3)^3+(3\cdot3)^3+\ldots+(10\cdot3)^3=\\\\=1^3\cdot3^3+2^3\cdot3^3+3^3\cdot3^3+\ldots+10^3\cdot3^3=\\\\=(1^3+2^3+3^3+\ldots+10^3)\cdot3^3\,\stackrel{\text{Series 2}}{=}\,(1+2+3+\ldots+10)^2\cdot27=\\\\\stackrel{\text{Series1}}{=}\,\left((10\cdot11)/(2)\right)^2\cdot27=55^2\cdot27=3025\cdot27=\boxed{81675}`