Find the sum of the n terms of the series $147 + 258 + 369.....$ ?

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Answer 1 · 2017-09-25T15:07:39

$n^3+9n^2+18n$

Each term can be represented by:

$[n* (n+3)*(n+6)]$

Check:
second term: n = 2

$(2* (2+3)*(2+6)) => (2*5*8)$

Expand:

$[n* (n+3)*(n+6)]=> n^3+9n^2+18n$

nth term $n^3+9n^2+18n$

Sum of n terms:

$1/4n(n+7)(n+6)(n+1)$

Find the sum of the n terms of the series 1*4*7 + 2*5*8 + 3*6*9.....1*4*7 + 2*5*8 + 3*6*9.....?