jumlah 50 suku pertama deret log5+log55+log605+log6655+.... adalah...
Matematika
dewimaesyaroh
Pertanyaan
jumlah 50 suku pertama deret log5+log55+log605+log6655+.... adalah...
1 Jawaban
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1. Jawaban hendrisyafa
= log 5 + log 5.11 + log 5.11²+ log 5.11³ + log 5.11⁴..
= log 5 + (log 5 + log 11) + (log 5 + log 11²) + (log 5 + log 11³) + (log 5+log 11⁴)..
= log 5 + log 5 + log 5 + log 5 + log 5 + log 11 + 2 log 11 + 3 Log 11 + 4 log 11
= 4 log 5 + 10 log 11
Log 5 --> S1 = 1
S2 = 2
S50 = 50 --> S50 utk log 5 = 50 log 5
Log 11 --> u1 = 0
u2 = 1 --> s2 = 1
u3 = 2 --> s3 = 3
u4 = 3 --> s4 = 6
u5 = 4 ---> s5 = 10
u50 = 49 --> s50 = 1/2 n (a+u50)
= 1/2. 50 (0+49)
= 1225 ----> S50 utk log 11 = 1225 log 11
S50 = 50 log 5 + 1225 log 11