Question #348708

Find the value of a2 for the recurrence relation an=17an-1+30n, where a0=3



Find the value of a3 for the recurrence relation an=17an-1+30n, where a0=3



Find the value of a1 for the recurrence relation an=17an-1+30n, where a0=3



What would be the hypothesis of the mathematical induction for x(x + 1) < x! , where x ≥ 7?



If P(k) = k2(k + 2)(k – 1) is true, then what is P (k + 1)?

1
Expert's answer
2022-06-09T14:37:57-0400

1.


a1=17(3)+30(1)=81a_1=17(3)+30(1)=81

a2=17(81)+30(2)=1437a_2=17(81)+30(2)=1437

2.


a3=17(1437)+30(3)=24519a_3=17(1437)+30(3)=24519

3.


a1=17(3)+30(1)=81a_1=17(3)+30(1)=81

4.

It is assumed that at x=k,x = k, P(k)P(k) holds


k(k+1)<k!k(k+1)<k!



5.

If P(k)=k2(k+2)(k1)P(k) = k^2(k + 2)(k – 1) is true, then it must be shown that P(k+1)P(k + 1) is true, namely, that

(k+1)2(k+1+2)(k+11)(k+1)^2(k+1 + 2)(k+1 – 1)

is also true.

Simplify


k(k+1)2(k+3)k(k+1)^2(k+3)

is also true.



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