Find sum of $n$ terms:
$12+14+24+58+164+\cdots$
I have tried my best but could not proceed
[Math] Find sum of $n$ terms of the series $12+14+24+58+164+\cdots$
sequences-and-seriessummation
sequences-and-seriessummation
Find sum of $n$ terms:
$12+14+24+58+164+\cdots$
I have tried my best but could not proceed
Best Answer
You can do this by grouping terms and using the geometric sum formula: $$2[\{6+(1-1)\}+\{6+(3-2)\}+\{6+(9-3)\}+\{6+(27-4)\}+\dots]$$ $$=2[6n+(1+3+9+27+...)-(1+2+3+4+...)]$$ $$=2\bigg[6n+\frac{3^n-1}{3-1}-\frac{n(n+1)}{2}\bigg]$$ $$=12n+3^n-1-n^2-n$$ $$=11n+3^n-1-n^2$$