Bantu jawab no 3 pls​

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Bantu jawab no 3 pls​

Bantu jawab no 3 pls​

Jawaban:

5 + 9 + 13 + 17 + … + (4n + 1) = 2² + 3n

  • Misal n = 1

4n + 1 = 2n² + 3n

4(1) + 1 = 2(1)² + 3(1)

5 = 5 → Terbukti

  • Untuk n = k

5 + 9 + 13 + 17 + … + (4k + 1) = 2k² + 3k

Benar. → Terbukti

  • Untuk n = k + 1

5 + 9 + 13 + 17 + … + (4k + 1) + (4(k + 1) + 1)= 2(k + 1)² + 3(k + 1)

k (2k + 3) + (4(k + 1) +1) = 2(k² + 2k + 1) + 3k + 3

2k² + 3k + 4k + 4 + 1 = 2k² + 4k + 2 + 3k + 3

2k² + 7k + 5 = 2k² + 7k + 5 → Terbukti