Matrices & Determinants · Determinant with summation of terms

f : \mathbb{N} \to \mathbb{Z}

is defined by

f(n) = \begin{vmatrix} n & -1 & -5\\ -2n^2 & 3(2k+1) & 2k+1\\ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix},\ k \in \mathbb{N}, \text{ and}

\displaystyle\sum_{n=1}^{k} f(n) = 98

, then

k

is equal to:

Video solution coming soon

We're animating every PYQ step by step. Subscribe to get them first.