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Here is another interesting pattern in Pascal's Triangle, which we will call the "hockey stick" property. C(i,r)=C(n+1,r+1) for 0≤r≤n. Below is an illustration where n=9 and r= 2 showing the "hockey stick" and the smaller "hockey stick" used in the induction step. ..C. C i=r Co C .c C₂ 2Co 2C₁ C₁ Co CoC 3C 3C 3C₂ 4C SCO SC₁/5C2₂/5C3 C4 3Cs C G C 4C1/C₂ S C C₁ с CC. Prove this result using mathematical induction. 2C₂ છે. છે. ઠે. . . . 3C₂ 4C3 4C4 C, /C₂ C₁ C₂ C C₂ C₁ C₂ C C₂ с с с с с с с C. 18 с, с, с CC. C. C

Here is another interesting pattern in Pascal's Triangle, which we will call the "hockey stick" property. C(i,r)=C(n+1,r+1) for 0≤r≤n. Below is an illustration where n=9 and r= 2 showing the "hockey stick" and the smaller "hockey stick" used in the induction step. ..C. C i=r Co C .c C₂ 2Co 2C₁ C₁ Co CoC 3C 3C 3C₂ 4C SCO SC₁/5C2₂/5C3 C4 3Cs C G C 4C1/C₂ S C C₁ с CC. Prove this result using mathematical induction. 2C₂ છે. છે. ઠે. . . . 3C₂ 4C3 4C4 C, /C₂ C₁ C₂ C C₂ C₁ C₂ C C₂ с с с с с с с C. 18 с, с, с CC. C. C

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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Here is another interesting pattern in Pascal's Triangle, which we will call the "hockey stick" property. C(i,r)=C(n+1,r+1) for 0≤r≤n. Below is an illustration where n=9 and r=2 showing the "hockey stick" and the smaller "hockey stick" used in the induction step. i=r - Co C₂ C. C 4C SCo 5C₁5C₂ C G/ C₁ 3C0 3₁ 3₂ 33 C₁ IC C C C. 1oC. 10.C 1C₂ Prove this result using mathematical induction. 6. 4C1/C₂/4C3 C4 Se S. S. S. S. S.S.S. 7.C.C..Cs /C₂ C₁ C₂ C C₂ C₂ C₂ C₂ C₂ KC C C C C C C₁ с с с C. C, C 18 C с с C с C C
Transcribed Image Text:Here is another interesting pattern in Pascal's Triangle, which we will call the "hockey stick" property. C(i,r)=C(n+1,r+1) for 0≤r≤n. Below is an illustration where n=9 and r=2 showing the "hockey stick" and the smaller "hockey stick" used in the induction step. i=r - Co C₂ C. C 4C SCo 5C₁5C₂ C G/ C₁ 3C0 3₁ 3₂ 33 C₁ IC C C C. 1oC. 10.C 1C₂ Prove this result using mathematical induction. 6. 4C1/C₂/4C3 C4 Se S. S. S. S. S.S.S. 7.C.C..Cs /C₂ C₁ C₂ C C₂ C₂ C₂ C₂ C₂ KC C C C C C C₁ с с с C. C, C 18 C с с C с C C
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