MATH 1B Lecture Notes - Lecture 22: Taylor Series, Tachykinin Receptor 1
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Math 1b: calculus - lecture 22: taylor series and polynomials. A: 7 x 6 pairs, but this estimate is too much. 7 x 6 / 2 = 21 ordered pairs. A: there are 7!/(7-3)! ways of picking 3 ordered things from 7 things. This overcounts by a factor of 6, or 3!. In fact, the number of ways of picking k unordered things from n things where n and k {0, , n} is : = n! ** note that (n written, like a fraction without the fraction line: is read as n choose k and that the n and k should be in the same column when. A: we have (1+x)6 = 1 + 6x + (6. = 1 + 6x + 15x2 + 20x3 + 15x4 + 6x5 + x6: x3 + (6, x4 + (6, x5 + x6. Why? k+1): + (n k+1) = (n+1. [1 + ((n-k)/(k+1))] (note that 1 can be rewritten as (k+1)/(k+1))
