Jumlah deret tak hingga x - 1/5 x^2 + 3/25 x^3 - 9/125 x^4 + .... = 1/2, maka x=?
Matematika
Feliciaayang
Pertanyaan
Jumlah deret tak hingga x - 1/5 x^2 + 3/25 x^3 - 9/125 x^4 + .... = 1/2, maka x=?
1 Jawaban
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1. Jawaban Anonyme
Deret Geometri Tak Hingga
1/3 x - 1/5 x² + 3/25 x³ - 9/125 x⁴ + ... = 1/2
a = 1/3 x
r = U2/U1
r = -1/5 x² / 1/3 x
r = -3/5 x
S~ = a/(1 - r)
1/2 = (1/3 x) / (1 + 3/5 x)
Kali silang
2/3 x = 1 + 3/5 x
2/3 x - 3/5 x = 1
1/15 x = 1
x = 15 ✔