Jawab:
Induksi Matematika
1/1.2 + 1/2.3 + 1/3.4 + ... + 1/n(n + 1) = n/(n + 1)
• n = 1
1/1.2 = 1/(1 + 1)
1/2 = 1/2
tebukti
• n = k
1/1.2 + 1/2.3 + 1/3.4 + ... + 1/k(k + 1) = k/(k + 1)
• n = k + 1
ruas kiri = A
[1/1.2 + 1/2.3 + 1/3.4 + ... + 1/k(k + 1)] + 1/(k + 1)(k + 1 + 1)
= k/(k + 1) + 1/(k + 1)(k + 2)
samakan penyebut
= (k(k + 2) + 1) / (k + 1)(k + 2)
= (k² + 2k + 1) / (k + 1)(k + 2)
= (k + 1)² / (k + 1)(k + 2)
= (k + 1) / (k + 2)
ruas kanan = B
(k + 1)/(k + 1 + 1)
ruas kiri = ruas kanan
A = B
t3rBu|<Tí
induksi
Penjelasan dengan langkah-langkah:
1/(1.2) + 1/(2.3) + 1/(3.4) + . . . + 1/ n(n+1) = n/ (n + 1)
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Jawab:
Induksi Matematika
1/1.2 + 1/2.3 + 1/3.4 + ... + 1/n(n + 1) = n/(n + 1)
• n = 1
1/1.2 = 1/(1 + 1)
1/2 = 1/2
tebukti
• n = k
1/1.2 + 1/2.3 + 1/3.4 + ... + 1/k(k + 1) = k/(k + 1)
• n = k + 1
ruas kiri = A
[1/1.2 + 1/2.3 + 1/3.4 + ... + 1/k(k + 1)] + 1/(k + 1)(k + 1 + 1)
= k/(k + 1) + 1/(k + 1)(k + 2)
samakan penyebut
= (k(k + 2) + 1) / (k + 1)(k + 2)
= (k² + 2k + 1) / (k + 1)(k + 2)
= (k + 1)² / (k + 1)(k + 2)
= (k + 1) / (k + 2)
ruas kanan = B
(k + 1)/(k + 1 + 1)
= (k + 1) / (k + 2)
ruas kiri = ruas kanan
A = B
t3rBu|<Tí
Jawab:
induksi
Penjelasan dengan langkah-langkah:
1/(1.2) + 1/(2.3) + 1/(3.4) + . . . + 1/ n(n+1) = n/ (n + 1)