Chef and Scores

Chef is addicted to checking cricket scores. One fine day, he dreams of a world cup consisting of infinite number of matches. His excitement either remains the same or increases after every match. He checks the score of the $1^{st}$ match $1$ time. His excitement now increases and he checks score of $2^{nd}$ match $2$ times. So, score of $\textbf{i}^{th}$ match is checked greater or equal times t