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CS417 - Coggle Diagram

- - - - Base 16 (hexadecimal)
  - - - optional:
        
        remembrance scheme: mclaughlin
- - - - ex:
        
        meaning of a symbol
    - - Σ
        
        add all numbers starting from bottom(0 if not noted)
        until top
        
        optional note
        
        its like a loop
- - - - r*Sn
        
        ar+ar^2+ar^3+...+ar^n-1+ar^n
        
        S - rS
        
        a + ar + ar^2 +...+ar^n-2+ar^n-1
        -ar+ar^2+ar^3+...+ar^n-1+ar^n
        = a - ar^n
        
        S - rS = 1-r^n
        
        6:factor lhs
        
        1 more item...
        
        5:set result equal to Sn - rSn
        
        4:subtract rSn from original Sn
        
        3:expand terms
        
        2:multiply Sn by r
      - 1: series definition
- - - - add it to itself
        
        2Sn = n+ n-1 + n-2 + ....4+3+2+1+ n+ n-1+n-2+...+4+3+2+1
        
        reverse one of them
        
        2Sn = n+ n-1 + n-2 + ....4+3+2+1
        
        +1+2+3+4+n-1+n-2+n
        
        group them
        
        2Sn =
        1 + 2 + 3 + 4 +... + n
        +n + n-1 + n-2 + n-3 +... + 1
        = n+1 + n+1 + n+1 + n+1 +...+ n+1
        or: n * (n+1)
        
        simplify
        
        1 more item...
- - - - weak induction
        
        two steps: