Tentukan jumlah dari deret geometri 27+9+3+1+….+1/81
Jawab:
Penjelasan dengan langkah-langkah:
a = 27
r = U2/U1
r = 9/27
r = 1/3
Un = 1/81
a . rⁿ⁻¹ = 1/81
27 . (1/3)ⁿ⁻¹ = 3⁻⁴
3³ . (3⁻¹)ⁿ⁻¹ = 3⁻⁴
3³⁻ⁿ⁺¹ = 3⁻⁴
4 – n = -4
4 + 4 = n
n = 8
Sn = a . (1 – rⁿ)/(1 – r)
S8 = 27 . (1 – (1/3)⁸)/(3/3 – 1/3)
S8 = 27 . (6.561/6.561 – 1/6.561) / (2/3)
S8 = 27 . 6.560/6.561 . 3/2
S8 = 3.280/81
S8 = 40 40/81
Detail jawaban
Kelas 9
Mapel 2 – Matematika
Bab 2 – Barisan dan Deret Bilangan
Kode Kategorisasi : 9.2.2
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