Sequence and Series (2)

Question 1

First three terms are (k+4), k and (2k-15), show that k^2 - 7k - 60 = 0

Answer 1

k/(k+4) = (2k-15)/k
k^2 = 2k^2 + 8k - 15k - 60
k^2 - 7k - 60 = 0

Question 2

k/(k+4) = (2k-15)/k
k^2 = 2k^2 + 8k - 15k - 60
k^2 - 7k - 60 = 0

Answer 2

First three terms are (k+4), k and (2k-15), show that k^2 - 7k - 60 = 0

Question 3

20C7

Answer 3

20!/(7!13!)

Question 4

Another way of writing n! in nCr

Answer 4

n(n-1)(n-2)(n-3)!

Question 5

n(n-1)(n-2)(n-3)!

Answer 5

Another way of writing n! in nCr

Question 6

In the binomial expansion of (1+x)^n, where n>=4, the coefficient of x^5 is two times greater than the coefficient of x^4.

Answer 6

nC5 = 2 * nC4

Question 7

In the binomial expansion of (1+5x)^n, where n>=3, the coefficient of x^3 is the difference between 32 times the coefficient of x^2 and 95 times the coefficient of x

Answer 7

nC3 * 5^3 = (32 * nC2 * 5^2) - (95 * nC2 * 5^1)

Question 8

Find the first five terms in the binomial expansion of (4+3x)^6 in ascending powers of x

Answer 8

(6C0)(4^6)(3x^0) + (6C1)(4^5)(3x) + (6C2)(4^4)(3x^2) + (6C3)(4^3)(3x^3) + (6C4)(4^2)(3x^4)

Question 9

The coefficient of the x^3 term in the binomial expansion of (1+px)^7 is 280. Find value of p

Answer 9

(7C3)(px)^3
35p^3x^3 = 280x^3
Then solve

Question 10

Find the coefficient of x^9 in the expansion (4-2x)^11?

Answer 10

(11C9)(4^2)(-2x^9)

Question 11

Get (4+3x)^(1/2) in the form (1+x)^n

Answer 11

(4^(1/2) (1+(3/4)x)^(1/2))

2(1+(3/4)x)^1/2

Question 12

Find the binomial expansion of (1+x)^-2 up to and including the term x^3

Answer 12

1 + (-2)x + ((-2)(-3))/12 + ((-2)(-3)(-4))/123

Question 13

The first three terms of (1+6x+12x^2+8x^3)(1+2x+3x^2+4x^3+…)

Answer 13

1(1+2x+3x^2) + 6x(1+2x) + 12x^2(1)

Question 14

Get the percentage error

Answer 14

|(real value - estimate)/real value|

Question 15

|(real value - estimate)/real value|

Answer 15

Get the percentage error

Question 16

Validity of (1+x)^-2

Answer 16

|x|<1

Question 17

|x|<1

Answer 17

Validity of (1+x)^-2

Question 18

Validity of (1+2x)^1/2

Answer 18

|x|<1/2

Question 19

|x|<1/2

Answer 19

Validity of (1+2x)^1/2

Question 20

Find the coefficient of x^10 in the expansion of (1-2x)^5 (2+x)^7

Answer 20

Find the coefficients of:
(1-2x)^3 * (2+x)^7
(1-2x)^4 * (2+x)^6
(1-2x)^5 * (2+x)^5
Then add them together