Sequences

Arithmetic sequences:

Definition: A sequence is arithmetic if the differences between consecutive terms are the same. Thus the sequence a(1), a(2), a(3) ....... a(n).... is arithmetic if there is a number d such that a(2) -a(1)=d,     a(3) -a(2) =d, and a(4) - a(3) =d and so on. The number D is the common difference of the arithmetic sequence.

Geometric sequences:

A sequence is geometric if the ratios of consecutive terms aren't the same
A(2)/a(1) = r,  a(3) / a(2) = r, a(4) / a(3) = r.... (R cannot = 0)
The number are is the common ratio of the sequence

Summation

Sequences and Summation

In this lesson we learned about infinite and finite sequences, factorials, summation notation, and properties of sums.

Infinte sequence:
A function whose domain is the set of positive integers. The function values a(1) a(2)....a(n)
Be sure to remember that n represents any positive real number and is exponential as it grows.

Finite sequence:
 if the domain of the function consists of the first n positive integers only.
Test for this first.

Factorial:
 if n is a positive integer, n factorial is defined by n! = 1x2x3x4 (n-1) x n

Summation notation:
The sum of the first n terms of a sequence.
Use the equations.

Kobe vs Lebron

It has long been a heated debate whether Lebron (the traitor) is better then Kobe Bryant (the black mamba). Seeing as though both these players are superstars as indicated by their first name trademarks, it is easy to see why this debate exists today. Today I will put this debate to rest using statistical comparison to decifer whether Lebron really sucks as much as I know he does.

NBA Championships Kobe Bryant 5      LeBron James 2   NBA Seasons Kobe Bryant 18                   LeBron James 11            Playoffs Played Kobe Bryant 15                LeBron James 8         All-Star Games Kobe Bryant 16                 LeBron James 10           Honors and Awards Season MVP Kobe Bryant 1 LeBron James 4     Finals MVP Kobe Bryant 2   LeBron James 2   All-NBA First Team Kobe Bryant 11            LeBron James 7        All-NBA Teams (Total Selections) Kobe Bryant 15                LeBron James 9          All-Defensive First Team Kobe Bryant 9          LeBron James 5      All-Defensive Teams (Total Selections) Kobe Bryant 12             LeBron James 5      Scoring Leader Kobe Bryant 2   LeBron James 1 Rookie of The Year Kobe Bryant 0 LeBron James 1   NBA Regular Season Stats Stats Per Game Points Per Game Kobe Bryant 25.5   LeBron James 27.5   Rebounds Per Game Kobe Bryant 5.3   LeBron James 7.2   Assists Per Game Kobe Bryant 4.8   LeBron James 6.9   Steals Per Game Kobe Bryant 1.5   LeBron James 1.7   Blocks Per Game Kobe Bryant 0.5   LeBron James 0.8   Totals Stats Total Points Kobe Bryant 31,700   LeBron James 22,447   Total Rebounds Kobe Bryant 6,601   LeBron James 5,913   Total Assists Kobe Bryant 5,925   LeBron James 5,636   Total Steals Kobe Bryant 1,835   LeBron James 1,398   Total Blocks Kobe Bryant 620   LeBron James 665   Total Games Kobe Bryant 1,245   LeBron James 816   Percentages Field Goal Percentage Kobe Bryant .454   LeBron James .495   3-Point Percentage Kobe Bryant .335   LeBron James .339   Free Throw Percentage Kobe Bryant .838   LeBron James .747   NBA Playoffs Stats Stats Per Game Points Per Game Kobe Bryant 25.6   LeBron James 28.1   Rebounds Per Game Kobe Bryant 5.1   LeBron James 8.6   Assists Per Game Kobe Bryant 4.7   LeBron James 6.7   Steals Per Game Kobe Bryant 1.4   LeBron James 1.7   Blocks Per Game Kobe Bryant 0.7   LeBron James 0.9   Totals Stats Total Points Kobe Bryant 5,640   LeBron James 3,871   Total Rebounds Kobe Bryant 1,119   LeBron James 1,191   Total Assists Kobe Bryant 1,040   LeBron James 924   Total Steals Kobe Bryant 310   LeBron James 236   Total Blocks Kobe Bryant 144   LeBron James 128   Total Games Kobe Bryant 220   LeBron James 138   Percentages Field Goal Percentage Kobe Bryant .448   LeBron James .472   3-Point Percentage Kobe Bryant .331   LeBron James .322   Free Throw Percentage Kobe Bryant .816   LeBron James .749   I must digress a little bit. It seems Lebron is not as bad as I thought. Although he is much younger then Kobe and still has a lot to prove. His game to game statistics are up to par with Mr. Bryant. His legacy will ultimately depend on the amount of championships he wins and how long he can sustain this high level of play. Could it be that Lebron is really the king? No that God. I love Jesus thank you.