You may also like
Telescoping Series
Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
Climbing Powers
$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?
Age 16 to 18 Challenge Level:
If you can solve quadratic equations and you know what powers of
numbers are then you can solve this problem. Just think about what
numbers raised to what powers give the value one. Take care to
check all the possibilities.
Copyright © 1997 - 2019.
University of Cambridge. All rights
reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.