Question

Bantuin yaa beserta caranya
1.) Buktikan 1+2+3+... +n=1/2 n ( n + 1 ) dengan cara rumus n = k + 1

Answer 1

Verified answer

# Langkah(1): buktikan n=1
1+2+3+...+n=1/2n(n+1)
n=1/2n(n+1)
1 = 1/2(1) (1+1)
1 = 1
#langkah(2): n=k
1+2+3+....+k=1/2k(k+1)
#langkah(3): n=k+1
1/2k(k+1)+n=1/2n(n+1) [hasil langkah 2+rumus]
1/2k(k+1)+(k+1)=1/2(k+1)((k+1)+1)
1/2k(k+1)+(k+1)=(1/2k+1/2)(k+2)
1/2k(k+1)+(k+1)=1/2(k+1)(k+2)
(k+2)/2 (k+1) = (k+2)/2 (k+1) [terbukti]