How to find the nth term of the series can anyone explain
1, 5, 13, 27, 48, 78, 118, 170, 235, 315, 411, 525, 658, 812, 988, 1188, 1413, 1665, …
It’s ans is n(n+2)(2n+1)/8 But how?
This sequence looks like the Friedreich’s formula for counting the number of triangles in a triangle which says,
If {T_n} represents number of Triangles in a triangle of n unit lengths, then,
{T_n} = \left \lfloor n(n+2)(2n+1)/8 \right \rfloor
A good derivation is given here.
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