Buktikan dengan induksi matematika
4+6+8+....+(2n+2)=n²+3n![]()
4+6+8+....+(2n+2)=n²+3n
Penjelasan dengan langkah-langkah:
[tex]a. \: n = 1 \\ 2n + 2 = {n}^{2} + 3n \\ 2(1) + 2 = {1}^{2} + 3(1) \\ 2 + 2 = 1 + 3 \\ 4 = 4 \: (benar) \\ \\ b. \: n = k \\ 2k + 2 = {k}^{2} + 3k \\ \\ c. \: n = k + 1 \\ (2k + 2) + 2(k + 1) + 2 = {(k + 1)}^{2} + 3(k + 1) \\ {k}^{2} + 3k + 2k + 2 + 2 = {k}^{2} + 2k + 1 + 3k + 3 \\ {k}^{2} + 5k + 4 = {k}^{2} + 5k + 4 \: (benar) [/tex]
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