Buktikan Bahwa 1x2+2x3+3x4+.....+n(n+1)=1/3n(n+1)(n+2)

Induksi Matematika
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(1x2) +(2x3)+(3x4)+...+ n(n+1) = 1/3 n(n+1)(n+2)
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langkah 1) n =1 --> 1(1+1) = 1/3 (1)(1+1)(1+3) --> 2 = 1/3 (6) (benar)
langkah 2) n = k -->
(1x2) +(2x3)+(3x4) +...+ k(k+1) = 1/3 k(k+1)(k+2)

langkah 3) n = k +1
1/3  k(k+1)(k+2) + (k+1)(k+1+1) = 1/3  (k+1)(k+1+1)(k+1+2)
1/3 k(k+1)(k+2) + (k+1)(k+2)  = 1/3 (k+1)(k+2)(k+3)
1/3(k+1)(k+2)[ k +3]  = 1/3 (k+1)(k+2)(k+3)
ruas kiri = ruas kanan
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