1.) buktikan bahwa barisan/deret berikut: 1² + 2² + 3² + 4² + ... + n² = n (n+1)(2n+1)/6 bernilai untuk semua n bilangan asli. 2.) buktikan bahwa deret/barisan

Induksi Mat
1)
1²+2²+3²+...+n² = n(n+1)(2n+1)/6
n = 1 (benar)
n= k --> 1²+..+k² = k(k+1)(2k+1)/6
n= k+1 --> k² + (k+1)² = (k+1)(k+1+1)(2(k+1)+1) / 6
k(k+1)(2k+1)/6 +(k+1)² = (k+1)(k+2)(2k+2+1)/6
1/6 {k(k+1)(2k+1) + 6(k+1)²} = 1/6 (k+1)(k+2)(2k+3)
1/6 {(k+1){ k(2k+1) + 6(k+1)} = 1/6(k+1)(k+2)(2k+3)
1/6 {(k+1) { 2k²+k + 6k + 6}} = 1/6(k+1)(k+2)(2k+3)
1/6 {(k+1) (2k² + 7k + 6)} = 1/6 k+1)(k+2)(2k+3)
1/6 {(k+1)(k+2)(2k +3)} = 1/6  (k+1)(k+2)(2k+3)
TerBuktI
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2)
1,2 + 2.3 + 3.4 + ..+n(n+1) = 1/3 (n(n+1)(n+2))
n = 1 (benar)
n= k --> 1.2 + 2.3 +..+ k (k+1) = 1/3  k(k+1)(k+2)
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(k+1)(k+2) + 3(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)
terbukTi