1a. Proof by induction: For every positive integer
n,
1•3•5...(2n-1)=(2n)!/(2n•n!). Please explain what the exclamation
mark means. Thank you for your help!
1b. Proof by induction: For each integer n>=8,
there are nonnegative integers a and b such that n=3a+5b
Prove these scenarios by mathematical induction:
(1) Prove n2 < 2n for all integers
n>4
(2) Prove that a finite set with n elements has 2n
subsets
(3) Prove that every amount of postage of 12 cents or more can
be formed using just 4-cent and 5-cent stamps
let G = D2n =
{e,r,r^2,...,rn-1,s,sr,sr2,..,srn-1}
a diedergroup of order 2n, where n >=3
(a) prove that [G,G] = <r2>
(b) prove that G/[G,G] consists of two elements if n is uneven and
4 elements if n is even