Author: cburkh04

Mathematical Induction Example
1/1*2 + 1/2*3 + … + 1 / n*(n+1) = n/n+1 for n > 1
Basis Step: n = 1
1/1*2 = 1/2
P(n) = n/n+1
P(1) = 1/1+1 or 1/2
1/2 = 1/2
Inductive Step:
If:
1/1*2 + 1/2*3 + … + 1 / k*(k+1) = k/k+1
Then:
1/1*2 + 1/2*3 + … + 1 / (k+1)*(k+2) = (k+1)/(k+2)
Proof:
k/k+1 + 1 / (k+1)*(k+2) = (k+1)/(k+2)
Simplify…
—————————————————————
Binomial Theorem
In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. Its simplest version sayswhenever n is any non-negative integer, the number

Paths and Cycles
Paths
Starting at one vertex and ending at another
Cycles
Starting at one vertex and ending at the same one.
Euler Cycle (circuit)
A cycle traversing all edges of the graph exactly once
Euler Path (not a cycle)
A path traversing all edges of the graph exactly once
Connected multigraph has a Euler cycle if and only if each of its vertacies has an even degree
Hamilton Cycle
Visits every vertex of the graph before returning to the original vertex on the last step.
Hamilton Path
Visits every vertex exactly once.
————————————————————-
Permutations and Combinations
Permutation—of distinct objects is an ordered arrangement of the objects
= n!
Number of r permutations in an n-element set:
n! / (n-r)!
Combinations—of elements of a set is an unordered selection of r elements from the set
C(n,r) = n! / r!(n-r)!z