Question

Find the sum of the n therm of the following

2 + 10 +30 +68 +130 + ...
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Answer 1

Hi,

Explanation:

`2=1^3+1\\10=2^3+2\\30=3^3+3\\...\\a_n=n^3+n\\\\\displaystyle \sum_(i=1)^n\ (i^3+i)=\sum_(i=1)^n\ i^3+ \sum_(i=1)^n\ i\\\\\\=((n(n+1))/(2))^2 +(n(n+1))/(2) \\\\=(n(n+1))/(2) ((n(n+1))/(2) +1)\\\\=(n(n+1))/(4) (n^2+n+2)`

Answer 2

240

Explanation:

2 + 10 = 12 +30 = 42 + 68 = 110 + 130 =240