Скачать или смотреть Can I Solve My Previous Problem With OTHER METHODS? (2 More)

0:00 Explaining the problem and my previous video
1:37 Method 1. Recurrence relation method
10:36 Method 2. Direct calculation using factorial notation of binomial coefficients

My special thanks to @Griffith who provided the second method.

Link to the previous video (guessing & induction proof):    • Summation Involving BINOMIAL COEFFICIENTS  

Hello there. It turned out that the problem in my previous video, which I solved by guessing and proving by mathematical induction, can be also solved by two other methods. The first method is recurrence relation method. However, the recurrence relation won't be some "easy" or "conventional" ones, hence we need a clever idea to reduce it to simpler relation. The second method is direct calculation using factorial notation of binomial coefficients, also with a clever idea to carry out the resulting summation of polynomial of k.

#combinatorics #sequences #BinomialCoefficients #combination #summation #sigma #RecurrenceRelation #factorial #TelescopingSum

-------------------------------------------------------------------------

CORNERSTONES OF MATH features quality math problems to strengthen your math fundamentals and problem-solving ability. Problems are generally on high school level (with some deviations), spanning over topics such as algebra, discrete mathematics, calculus, geometry, statistics, trigonometry, etc. I hope that this channel provides some intellectual pleasure and make you appreciate the beauty of math itself.

Please consider giving a Like to this video and Subscribing to my channel, it really means a lot for the creator like me, and you will be introduced to many more interesting math videos!