On day one, there are 100 particles in a laboratory experiment. On day n n n , where n ≥ 2 n \geq 2 n ≥ 2 , one out of every n n n particles produces ...

Suppose $$ x_1, x_2, x_3, \dots, x_{100} $$ are in arithmetic progression such that $$ x_5 = -4 $$ a...

Consider the sequence $$ t_1 = 1 $$, $$ t_2 = -1 $$, and $$ t_n = \left(\frac{n-3}{n-1}\right) t_...

The sum of the infinite series $$ \frac{1}{5} \left( \frac{1}{5} - \frac{1}{7} \right) + \left( \...

For some positive and distinct real numbers $$ x $$, $$ y $$, and $$ z $$, if $$ \frac{1}{\sqrt{x...

A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on t...

Let both the series $$a_1, a_2, a_3, \dots$$ and $$b_1, b_2, b_3, \dots$$ be in arithmetic progress...