1)Find the third iterate x3 of f(x)=x2-4 for an initial value of x0=2
A)-4
B)4
C)12
D)-12
I chose C
2)Use Pascal's triangle to expand:(w-x)5
This ones long so I chose w5-5w4x+10w3x3-10w2x4+5wx4-x5
3)Use the binomial Theorem to find the third term in the expression of:(n-2p)6
A)60n4p2
B)120n3p3
C)-12n5p
D)-160n2p4
I chose C
4)Which is not a counterexample to the formula:1^2+3^2+5^2+...+(2n-1)2=n(2n+1/3
A)n=3
B)n=2
C)n=1
D)n=4
I chose C
5)In an induction proof of the statement 4+7+10+...+(3n-1)=n(3n+5)/2
the first step is to show that the statement is true for some integers n.
Note:3(1)+1=1[3(1)+5]/2 is true. Select the steps required to complete the proof.
A)Show that the statement is true for any real number k. Show that the statement is true for k+1.
B)Assume that the statement is true for some positive integer k. Show that the statement is true for k+1.
C)Show that the statement is true for some positive integers k. Give a counterexample.
D)Assume thst the statement is true for some positive integers k+1. Show that the staement is true for k.
I don't know
Thank you SO much Reiny for helping me. I'm not looking for anyone to give me the answer because Ive done the work and what ever I answered is my BEST answer and I can't afford to get them wrong so thanks for all your help from the bottom of my heart.
1. do you mean Xn+1 = Xn^2 - 4 ?
X0 = 2
X1 = 4-4 = 0
X2 = 0-4 =-4
X3 = 16-4 = 12
2. row five 1 5 10 10 5 1
wherever you have an odd power of x, you will have a minus sign with a =w and b = -x
w^5 -5w^4x^1+10w^3x^2-10w^2x^3+5wx^4-x^5
3. (15a^4 b^2) where a =n and b = -2p
(15)n^4(-2p)^2
=60 n^4 p^2
4.Yes c, but PLEASE use parentheses carefully and use ^ for to the power! I am spending all my time figuring out what you mean.
5. I do not understand. Are you sure it is not (3n+1)?
5.Assuming this works, find out
Using (3n+1) which is 3(n+1)+1 at n+1 which is 3n+4
Sum at(n+1) = sum at n + 3(n+1)+1
(n+1)(3(n+1)+5)/2 =n(3n+5)/2 + 3n+4 multiply by two and simplify
(n+1)(3n+8) = 3n^2 + 5n +6n +8
or
3n^2 + 11n + 8 = 3n^2 + 11n + 8
Lo and behold, it is true
1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16
1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16
1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16
1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16
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