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  3. 1.prove the following statements: . (a) if bn is r

1.Prove the following statements: . (a) If bn is recursively defined by bn =bn?1+3 for all integers n?1...

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Advance Math

1.Prove the following statements:

.

(a) If bn is recursively defined by bn =bn?1+3 for all integersn?1 and b0 =2,

then bn =3n+2 for all n?0.

.(b) If cn is recursively defined by cn =3cn?1+1 for allintegers n?1 and c0 =0,

then cn =(3n ?1)/2 for all n?0.

.(c) If dn is recursively defined by d0 = 1, d1 = 4 and dn =4dn?1 ?4dn?2 for all integers n ? 2,

then dn =(n+1)2n for all n?0.

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