1. what is the sequence Xn for n>= 0 is given by recurrencerelation X0 = 0, X
ID: 2939950 • Letter: 1
Question
1. what is the sequence Xn for n>= 0 is given by recurrencerelation X0 = 0, X1 = 3,Xn+2 =Xn+1 +2Xn, n>=0.
a) find X4.
b) find a formula for Xn in terms of n.
2. Give the x3 Y4 term of the followwing binomial expansion:
a)(x-y)7.
B(x+3y)7.
3. five objects are chosen from nine objects (as usual, the objectsare distinguishable,
and there is no replacement).
a) how many ways can this be done, if the order of choicematters?
b) how many ways can this be done, if the order of choice does notmatter?
4. prove by induction that for integers n,r with0<=r<=n the number of ways of arraging r a's and n-rb's in a line is binomial coefficient n
C
r.
(this is the number of words containing r a's and (n-r) b's)
to answer this we have to go back to the structure of a list. Aword of n+1 characters is obtained from a word with n characters byadding a character at the front.
so we have the following 2 possibilities for a word with n+1characters where w is a word and with n characters either aw orbw.
a) now use induction on the value n.
can some help the brother out cheap as it only counts to 3% of themodule so can some one do it cheaply or free if possible?
Explanation / Answer
1. what is the sequence Xn for n>= 0 is given by recurrencerelation X0 = 0, X1 = 3, Xn+2 =Xn+1 +2Xn, n>=0. a) find X4. b) find a formula for Xn in terms of n. 2. Give the x3 Y4 term of the followwing binomial expansion: a)(x-y)7. B(x+3y)7. 3. five objects are chosen from nine objects (as usual, the objectsare distinguishable, and there is no replacement). a) how many ways can this be done, if the order of choicematters? b) how many ways can this be done, if the order of choice does notmatter? 4. prove by induction that for integers n,r with0<=r<=n the number of ways of arraging r a's and n-rb's in a line is binomial coefficient n C r. (this is the number of words containing r a's and (n-r) b's) to answer this we have to go back to the structure of a list. Aword of n+1 characters is obtained from a word with n characters byadding a character at the front. so we have the following 2 possibilities for a word with n+1characters where w is a word and with n characters either aw orbw. a) now use induction on the value n. can some help the brother out cheap as it only counts to 3% of themodule so can some one do it cheaply or free if possible?
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