Question

Use iteration to guess an explicit formula for the sequence...

Materials for Reference:

Homework Problems Solve the following problems 1. Use iteration to guess an explicit formula for the sequence. Use the formulas from summation formula.pdf to simplify your answers whenever possible. (Follow the solution of exercise set 57-problem #5, on page A-43) dk-4dk-1+3, for all integers k2 2,where d1-2 2. Use iteration to guess an explicit formula for the sequence. Use the formulas from summation formula.pdf to simplify your answers whenever possible. (Follow the solution of exercise set 57-problem#12, on page A-44) tk tk-1+3k+1, for all integers k 21to 0 3. Given a recursive definition of the set of positive integers that are multiples of 5 4. Give a recursive definition for the set of all strings of O's and 1's for which all the 1's precede all the O's. 5. Give a recursive definition for the set of all strings of a's and b's that ends with an'a. TABLE 2 Some Useful Summation Formulae. Closed Form Sum Σ arkは0) arn+1 n(n +1 n(n )(2n + 1) 1 n-(n+1 k-1 (1-x) 5.0* 0 Tigran Sloyan From the definition of ck, we have that c,-1, c2 = 3+1, сз 3(3 + 1)+1=32 + 3+1, c4 = 3(32 + 3 + 1) + 1 33+32 +3 +1. From this first few termst becomes apparent that C 3132 +..+3+1for all k-k-2 It's easy to check by substitution that this sequence satisfies the given recurrence relation. RESULT 3k-1 5.0* 0 Manuel Fuenmayor S S-12k Sk-2 +2(k -1) +2(k) -S-3 + 2(k-2) + 2(k-1 ) + 2(k) -3+25% 3+2kk1) Skk(k+1)+3 Note the I have substituted 3 for S RESULT Sk-k(k +1) +3

Answer 1

Solution oV k-2. K-l K-l

2 2. 2- definition cf eckef ali positive inten ot