Buktikan melalui induksi matematika 1/1(2) + 1/2(3) + 1/3(4) +....+ 1/n(n+1) = n/n+1

1. untuk n = 1
1/1(2) = 1/(1+1)
1/2 = 1/2 (Terbukti)

2. untuk n = k
1/1(2)+1/2(3)+1/3(4)+...+1/k(k+1) = k/k+1
(Benar)

3. untuk n = k+1
1/1(2)+1/2(3)+1/3(4)+...+1/k(k+1)+1/(k+1)(k+1+1) = (k+1)/(k+1+1)
(k/k+1) + 1/(k+1)(k+2) = k+1/k+2
k²+2k+1/(k+1)(k+2) = k+1/k+2
(k+1)² / (k+1)(k+2) = k+1 / k+2
k+1 / k+2 = k+1 / k+2
(TERBUKTI)