1.2 + 2.3 + 3.4 +....+n(n+1)=1\3n(n+1)(n+2) tolong ya susah bgt..

1.2 + 2.3 + 3.4 + ... + n(n + 1) = 1/3 n(n + 1)(n + 2)

1) akan dibuktikan untuk n = 1 benar
1(1 + 1) = 1/3 . 1 (1 + 1)(1 + 2)
1(2) = 1/3 . 2 . 3
2 = 2 ==> (BENAR)

2) misal untuk n = k benar
1.2 + 2.3 + 3.4 + ... + k(k + 1) = 1/3 k(k + 1)(k + 2)
Akan dibuktikan untuk n = k + 1 benar
1.2 + 2.3 + 3.4 + .. + k(k+1) + (k+1)((k+1) + 1) = 1/3 (k + 1)((k + 1) + 1)((k + 1) + 2)
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....... 1/3 k (k + 1)(k + 2) ....... + (k + 1)((k + 1) + 1)
= k/3 (k + 1)(k + 2) + (k + 1)(k + 2)
= (k + 1)(k + 2) [k/3 + 1]
= (k + 1)(k + 2) (k + 3)/3
= 1/3 (k + 1) ((k + 1) + 1) ((k + 1) + 2)
(BENAR dan TERBUKTI)