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12, Show that ()() = (OC)- n-m' %3D 13. Show thet (A)

12, Show that ()() = (OC)- n-m' %3D 13. Show thet (A)

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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Number 12
3. Use the binomial theorem to find the coefficient of x³ in (x+2)13 4. JUse the binomial theorem to find the coefficient of x6 y in (3x- 2y). useful from time to time. For instance, you can use it if you ever (2a)* + 4(2a)°(-b)+6(2a)²(-bÝ + 4(2a)(-bỷ +(-b¢ For now we will be content to accept the binomial theorem wis (You will be asked to prove it in an exercise in Chapter 10.) You m expand an such as (x+ y)?. To do this, look at Row 1 t 2. Use the binomial theorem to find the coefficient of x³ y³ in (x+ y)13 10. Show that the formula k() = n(j) is true for all integers n,k with 0sks n. The Ineluston-4 3.7 The Inel Many eountin of two finite s First we must equal A and then get IA1+B counted ea +7xy For another example, (2a)+(-b))* (2a - b)4 %3D 16a –32a®b+24a²b² – 8ab³ + b4 %3D Therefor LAI+B Fa If Exercises for Section 3.6 1. Write out Row 11 of Pascal's triangle. No so Fa to th 5. Use the binomial theorem to show Eo4) = 2". 6. Use Definition 3.2 (page 85) and Fact 1.3 (page 13) to show 7. Use the binomial theorem to show E-, 3* () = 4". 8. Use Fact 3.5 (page 87) to derive Equation 3.3 (page 90). 9. Use the binomial theorem to show (6)–(1)+6)-(3)+(4) – …- -(-1)* (") =0, & form exclh in fa Cor Ex ma 11. Use the binomial theorem to show 9" = E"-,(-1)* (*)10"-k. 12, Show that ()() = OC). 13. Show that () = 6) + C) + () + () + 14. The first five rows of Pascal's triangle appear in the digits of powers of 11:11- 11 = 11, 112 = 121, 113 = 1331 and 114 = 14641, Why is this so? Why doestie pattern not continue with 11? th %3D (i • (";"). +...+
Transcribed Image Text:3. Use the binomial theorem to find the coefficient of x³ in (x+2)13 4. JUse the binomial theorem to find the coefficient of x6 y in (3x- 2y). useful from time to time. For instance, you can use it if you ever (2a)* + 4(2a)°(-b)+6(2a)²(-bÝ + 4(2a)(-bỷ +(-b¢ For now we will be content to accept the binomial theorem wis (You will be asked to prove it in an exercise in Chapter 10.) You m expand an such as (x+ y)?. To do this, look at Row 1 t 2. Use the binomial theorem to find the coefficient of x³ y³ in (x+ y)13 10. Show that the formula k() = n(j) is true for all integers n,k with 0sks n. The Ineluston-4 3.7 The Inel Many eountin of two finite s First we must equal A and then get IA1+B counted ea +7xy For another example, (2a)+(-b))* (2a - b)4 %3D 16a –32a®b+24a²b² – 8ab³ + b4 %3D Therefor LAI+B Fa If Exercises for Section 3.6 1. Write out Row 11 of Pascal's triangle. No so Fa to th 5. Use the binomial theorem to show Eo4) = 2". 6. Use Definition 3.2 (page 85) and Fact 1.3 (page 13) to show 7. Use the binomial theorem to show E-, 3* () = 4". 8. Use Fact 3.5 (page 87) to derive Equation 3.3 (page 90). 9. Use the binomial theorem to show (6)–(1)+6)-(3)+(4) – …- -(-1)* (") =0, & form exclh in fa Cor Ex ma 11. Use the binomial theorem to show 9" = E"-,(-1)* (*)10"-k. 12, Show that ()() = OC). 13. Show that () = 6) + C) + () + () + 14. The first five rows of Pascal's triangle appear in the digits of powers of 11:11- 11 = 11, 112 = 121, 113 = 1331 and 114 = 14641, Why is this so? Why doestie pattern not continue with 11? th %3D (i • (";"). +...+
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