Mathematics: Pattern question i guess ? i need part c) working : ))

Pattern question i guess ? i need part c) working

Ответ:

shay5878

13.03.2022

From "Series 1" we know, that:

$1+2+3+\ldots+n=\dfrac{n(n+1)}{2}$

and from "Series 2":

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

c)

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

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Ответ:

kamkamkab

22.02.2021

Mathematics

9 thousands 3 hundreds 2 tens 6 ones
or
9326

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Pattern question i guess ? i need part c) working : ))

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