Solving sequences an series#

Solving sequences an series#

With nearly 300 problems including hints, answers, and solutions, Methods of Solving Sequences and Series Problems is an ideal resource for those learning calculus, preparing for mathematics competitions, or just looking for a worthwhile challenge.

Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Convergence divergence calculator with steps Infinite series can be very useful for computation and problem solving but it is often one of the most.

Proof techniques are emphasized, with a variety of methods presented. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference. An arithmetic sequence is a series of numbers obtained by adding (or subtracting) the same value with each step. The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. c0 2, c1 0, cn cn 1 + 2cn 2 for every n 2. For each of the following recursively-defined sequences, use the method of generating functions to find an explicit formula for the nth term of the sequence. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. Related discussions A level maths Polynomials Geometric series homework help Finding the simplest equation for the sequence: 1, 5, 21, 85. A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. 7) Use the generalised binomial theorem to find hn, the coefficient of xn in h(x). This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications.