Explain step by step and thoroughly a Prove that nNi0.pdf

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Explain step by step and thoroughly. a) Prove that: nN,i=0ni2i=(n1)2n+1+2. b) Consider the sequence (si)iZ+defined by s1=1 and: n2..+ ,sn=2sn1+n. Show that sn=4sn2+(2n+n)2 and sn=8sn3+(4n+2n+n)(42+2). Likewise, express sn in terms of sn4 and n, and then in terms of sn5 and n. c) Using a) and b), can you guess sn in terms of sni,n and i? What expression do you get for sn when i=n1 ? Verify it by induction..

Explain step by step and thoroughly.
a) Prove that: nN,i=0ni2i=(n1)2n+1+2. b) Consider the sequence (si)iZ+defined by s1=1 and: n2..+
,sn=2sn1+n. Show that sn=4sn2+(2n+n)2 and sn=8sn3+(4n+2n+n)(42+2). Likewise, express sn in
terms of sn4 and n, and then in terms of sn5 and n. c) Using a) and b), can you guess sn in terms
of sni,n and i? What expression do you get for sn when i=n1 ? Verify it by induction.

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會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文

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會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽

會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽

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1. Explain step by step and thoroughly. a) Prove that: nN,i=0ni2i=(n1)2n+1+2. b) Consider the sequence (si)iZ+defined by s1=1 and: n2..+ ,sn=2sn1+n. Show that sn=4sn2+(2n+n)2 and sn=8sn3+(4n+2n+n)(42+2). Likewise, express sn in terms of sn4 and n, and then in terms of sn5 and n. c) Using a) and b), can you guess sn in terms of sni,n and i? What expression do you get for sn when i=n1 ? Verify it by induction.