1 Graphs 2 Functions And Their Graphs 3 Linear And Quadratic Functions 4 Polynomial And Rational Functions 5 Exponential And Logarithmic Functions 6 Trigonometric Functions 7 Analytic Trigonometry 8 Applications Of Trigonometric Functions 9 Polar Coordinates; Vectors 10 Analytic Geometry 11 Systems Of Equations And Inequalities 12 Sequences; Induction; The Binomial Theorem 13 Counting And Probability 14 A Preview Of Calculus: The Limit, Derivative, And Integral Of A Function A.1 Algebra Essentials A.10 Nth Roots; Rational Exponents A.2 Geometry Essentials A.3 Polynomials A.4 Synthetic Division A.5 Rational Expressions A.6 Solving Equations A.7 Complex Numbers; Quadratic Equations In The Complex Number System A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications A.9 Interval Notation; Solving Inequalities B The Limit Of A Sequence; Infinite Series expand_more
12.1 Sequences 12.2 Arithmetic Sequences 12.3 Geometric Sequences; Geometric Series 12.4 Mathematical Induction 12.5 The Binomial Theorem Chapter Questions expand_more
Problem 1AYU: The ______ ______ is a triangular display of the binomial coefficients. Problem 2AYU: ( n 0 )=and( n 1 )= . Problem 3AYU: True or False ( n j )= j! ( nj )!n! Problem 4AYU: The ______ ________ can be used to expand expressions like ( 2x+3 ) 6 . Problem 5AYU: In Problems 5-16, evaluate each expression. ( 5 3 ) Problem 6AYU: In Problems 5-16, evaluate each expression. ( 7 3 ) Problem 7AYU: In Problems 5-16, evaluate each expression. ( 7 5 ) Problem 8AYU: In Problems 5-16, evaluate each expression. ( 9 7 ) Problem 9AYU: In Problems 5-16, evaluate each expression. ( 50 49 ) Problem 10AYU: In Problems 5-16, evaluate each expression. ( 100 98 ) Problem 11AYU: In Problems 5-16, evaluate each expression. ( 1000 1000 ) Problem 12AYU: In Problems 5-16, evaluate each expression. ( 1000 0 ) Problem 13AYU: In Problems 5-16, evaluate each expression. ( 55 23 ) Problem 14AYU: In Problems 5-16, evaluate each expression. ( 60 20 ) Problem 15AYU: In Problems 5-16, evaluate each expression. ( 47 25 ) Problem 16AYU: In Problems 5-16, evaluate each expression. ( 37 19 ) Problem 17AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( x+1 ) 5 Problem 18AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( x1 ) 5 Problem 19AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( x2 ) 6 Problem 20AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( x+3 ) 5 Problem 21AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( 3x+1 ) 4 Problem 22AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( 2x+3 ) 5 Problem 23AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( x 2 + y 2 ) 5 Problem 24AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( x 2 y 2 ) 6 Problem 25AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( x + 2 ) 6 Problem 26AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( x 3 ) 4 Problem 27AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( ax+by ) 5 Problem 28AYU: In Problems 17-28, expand each expression using the Binomial Theorem. ( axby ) 4 Problem 29AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The... Problem 30AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The... Problem 31AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The... Problem 32AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The... Problem 33AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The... Problem 34AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The... Problem 35AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The 5th term... Problem 36AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The 3rd terms... Problem 37AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The 3rd term... Problem 38AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The 6th term... Problem 39AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The... Problem 40AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The... Problem 41AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The... Problem 42AYU: In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The... Problem 43AYU: Use the Binomial Theorem to find the numerical value of ( 1.001 ) 5 correct to five decimal places.... Problem 44AYU: Use the Binomial Theorem to find the numerical value of ( 0.998 ) 6 correct to five decimal places. Problem 45AYU: Show that ( n n1 )=nand( n n )=1 . Problem 46AYU: Show that if n and j arc integers with 0jn , then, ( n j )=( n nj ) Conclude that the Pascal... Problem 47AYU: If n is a positive integer, show that, ( n 0 )+( n 1 )++( n n )= 2 n [Hint: 2 n = ( 1+1 ) n ; now... Problem 48AYU: If n is a positive integer, show that ( n 0 )( n 1 )+( n 2 )+ ( 1 ) n ( n n )=0 Problem 49AYU: ( 5 0 ) ( 1 4 ) 5 +( 5 1 ) ( 1 4 ) 4 ( 3 4 )+( 5 2 ) ( 1 4 ) 3 ( 3 4 ) 2 +( 5 3 ) ( 1 4 ) 2 ( 3 4 )... Problem 50AYU: Stirling’s Formula An approximation for n! , when n is large, is given by n! 2n ( n e ) n ( 1+ 1... format_list_bulleted