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9. 2n (2) for for n ≥ 0

9. 2n (2) for for n ≥ 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you please help with #9? Please don't copy the answer from Chegg as it is wrong. TIA

Justify the equations in 6-9 either by deriving them from for- mulas in Example 9.7.1 or by direct computation from Theo- rem 9.5.1. Assume m, n, k, and r are integers. 6. (m+k₁) - = m + k, for m+k≥ 1 1 n+3 7. (+³) = (n+3)(n+2) 2 , for n ≥ -1 n+1 8. (7) = 1, for k-r≥0 k r 2n 9. (²2) for n ≥ 0 n
Transcribed Image Text:Justify the equations in 6-9 either by deriving them from for- mulas in Example 9.7.1 or by direct computation from Theo- rem 9.5.1. Assume m, n, k, and r are integers. 6. (m+k₁) - = m + k, for m+k≥ 1 1 n+3 7. (+³) = (n+3)(n+2) 2 , for n ≥ -1 n+1 8. (7) = 1, for k-r≥0 k r 2n 9. (²2) for n ≥ 0 n
Theorem 9.5.1 The number of subsets of size r (or r-combinations) that can be chosen from a set of n elements, ("), is given by the formula P(n,r) = first version r! or, equivalently, n! (-)- second version r!(n-r)! where n and r are nonnegative integers with r ≤n.
Transcribed Image Text:Theorem 9.5.1 The number of subsets of size r (or r-combinations) that can be chosen from a set of n elements, ("), is given by the formula P(n,r) = first version r! or, equivalently, n! (-)- second version r!(n-r)! where n and r are nonnegative integers with r ≤n.
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