5
Problems(4)
Geometric Series and Factorials
Source:
3/15/2010
A geometric series is one where the ratio between each two consecutive terms is constant (ex. 3,6,12,24,...). The fifth term of a geometric series is 5!, and the sixth term is 6!. What is the fourth term?
factorialratiogeometric series
Rows of Cocoa Pebbles
Source:
3/15/2010
Jerry is bored one day, so he makes an array of Cocoa pebbles. He makes 8 equal rows with the pebbles remaining in a box. When Kramer drops by and eats one, Jerry yells at him until Kramer realizes he can make 9 equal rows with the remaining pebbles. After Kramer eats another, he finds he can make 10 equal rows with the remaining pebbles. Find the smallest number of pebbles that were in the box in the beginning.
Nested Trigonometry
Source:
3/16/2010
There exist two positive numbers such that \sin(\arccos(\tan(\arcsin x)))\equal{}x. Find the product of the two possible .
trigonometryquadratics
Σ to ∞
Source:
3/20/2010
Evaluate: \sum\limits_{k\equal{}1}^\infty \frac{1}{k\sqrt{k\plus{}2}\plus{}(k\plus{}2)\sqrt{k}}