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11.9.2: Key Equations

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    116454
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    Key Equations

    Formula for a factorial 0!=1 1!=1 n!=n( n1 )( n2 )( 2 )( 1 ), for n2 0!=1 1!=1 n!=n( n1 )( n2 )( 2 )( 1 ), for n2
    recursive formula for nth term of an arithmetic sequence a n = a n1 +d , n2 a n = a n1 +d , n2
    explicit formula for nth term of an arithmetic sequence a n = a 1 +d(n1) a n = a 1 +d(n1)
    recursive formula for nthnth term of a geometric sequence a n =r a n1 ,n 2 a n =r a n1 ,n 2
    explicit formula for nth nth term of a geometric sequence a n = a 1 r n1 a n = a 1 r n1
    sum of the first n n terms of an arithmetic series S n = n( a 1 + a n ) 2 S n = n( a 1 + a n ) 2
    sum of the first n n terms of a geometric series S n = a 1 (1 r n ) 1r ,r1 S n = a 1 (1 r n ) 1r ,r1
    sum of an infinite geometric series with 1<r<1 1<r<1 S n = a 1 1r ,r1 S n = a 1 1r ,r1
    number of permutations of n n distinct objects taken r r at a time P(n,r)= n! (nr)! P(n,r)= n! (nr)!
    number of combinations of n n distinct objects taken r r at a time C(n,r)= n! r!(nr)! C(n,r)= n! r!(nr)!
    number of permutations of n n non-distinct objects n! r 1 ! r 2 ! r k ! n! r 1 ! r 2 ! r k !
    Binomial Theorem (x+y) n = k0 n ( n k ) x nk y k (x+y) n = k0 n ( n k ) x nk y k
    (r+1)th (r+1)th term of a binomial expansion ( n r ) x nr y r ( n r ) x nr y r
    probability of an event with equally likely outcomes P(E)= n(E) n(S) P(E)= n(E) n(S)
    probability of the union of two events P(EF)=P(E)+P(F)P(EF) P(EF)=P(E)+P(F)P(EF)
    probability of the union of mutually exclusive events P(EF)=P(E)+P(F) P(EF)=P(E)+P(F)
    probability of the complement of an event P(E')=1P(E) P(E')=1P(E)

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