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nomor 3 a

08 Jan

an=2an-1 + 1

solusi an= an (H) + an (P)

an (H) è an – 2an-1=0 , misal an= crn

crn – 2crn-1 = 0 dibagi crn

r – 2 = 0, r=2

an (H) = c2n

—————————————————

an (P) à an – 2an-1=1 ,

A – 2A = 1 , -A = 1 , A = -1

an= an (H) + an (P)

an= c2n -1

utk a1=1 à c21 -1 = 1

2c – 1 = 1 , 2c = 2 , c=1

Sehingga an= an (H) + an (P) = 1.2n -1

Solusi umum an= 2n -1

 
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Ditulis oleh pada Januari 8, 2012 in Matematika

 

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