List of top Mathematics Questions on sequences asked in Consortium of Medical Engineering and Dental Colleges of Karnataka Under Graduate Entrance Test

Using mathematical induction, the numbers $ a_n $ are defined by $ a_0 = 1, a_{n+1} = 3n^2 + n + a_n, (n \geq 0) $. Then, $ a_n $ is equal to
The value of \[ 1! + 2! + 2! + 3! + 3! + \cdots + n \cdot n! \] is:
The sum of the series \( (1 + 2) + (1 + 2 + 2^2) + (1 + 2 + 2^2 + 2^3) + \cdots \) up to terms is: