MarcKrishkeTest4Math1540

# MarcKrishkeTest4Math1540 - Math 1540 Test 2 Chapters 7 and...

This preview shows pages 1–3. Sign up to view the full content.

Math 1540 Test 2: Chapters 7 and 8 4/26/10 Name: 10-points each 1.) Starting with 0 n = , write up to 9 n = of Pascal’s triangle. Be sure to list each row by name. 1 0 1 1 1 1 2 1 2 1 3 3 1 3 1 4 6 4 1 4 1 5 10 10 5 1 5 1 6 15 20 15 6 1 6 1 7 21 35 35 21 7 1 7 1 8 28 56 70 56 28 8 1 8 1 9 36 84 126 126 84 36 9 1 9

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2.) Use Pascal’s triangle and the binomial theorem to expand the following. a . ) ( 29 5 5 4 3 2 2 3 4 5 5 4 3 2 2 3 4 5 5 4 3 2 2 3 4 5 5 4 3 2 5 5 5 5 3 (3 ) (3 ) (3 ) (3 ) (3 ) 1 2 3 4 5! 5! 5! 5! 243 81 27 9 3 1!4! 2!3! 3!2! 4!1! 243 5 81 10 27 10 9 5 3 243 405 270 90 t s t t s t s t s t s s t t s t s t s ts s t t s t s t s ts s t t s t s         - = - + - + -                 = - + - + - = - ⋅ + - + ⋅ - = - + - 2 3 4 5 15 t s ts s + - b.) ( 29 4 4 3 2 2 3 4 2 3 4 2 3 4 2 3 4 4 4 4 3 2 3 3 (2 ) 3 (2 ) 3(2 ) (2 ) 1 2 3 4! 4! 4! 81 27(2 ) 9 4 3 8 16 1!3! 2!2! 3!1! 81 4 54 6 36 4 24 16 81 216 216 96 16 z z z z z z z z z z z z z z z z z       - = - + - +             = - + ⋅ ⋅ - ⋅ ⋅ + = - ⋅ + ⋅ - ⋅ + = - + - + 3.) Write the first five terms of the given sequence. ( 29 2 .) 2 3 n a a n = + a 1 = (2 1 + 3) 2 = (2 + 3) 2 = 5 2 = 25 a 2 = (2 2 + 3) 2 = (4 + 3) 2 = 7 2 = 49 a 3 = (2 3 + 3) 2 = (6 + 3) 2 = 9 2 = 81 a 4 = (2 4 + 3) 2 = (8 + 3) 2 = 11 2 = 121 a 5 = (2 5 + 3) 2 = (10 + 3) 2 = 13 2 = 169 ( 29 2 .) 5 4 100 n
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 8

MarcKrishkeTest4Math1540 - Math 1540 Test 2 Chapters 7 and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online