3+7+11....+(4n-1)=2nkuadrat +n buktikan kebenarannya

jawab

3 + 7 + 11 + ... + (4n -1) = 2n² + n

n = k 
3+ 7 + 11 + ...+(4k - 1) = 2k² + k

n=k + 1
{3 +7+ 11 + ...+ (4k - 1)} + 4{k+1} - 1  = 2(k + 1)² + (k + 1)
2k² + k + 4k + 4 - 1  = 2(k+ 1)²  + (k + 1)
2k² + 5k + 3 = 2(k+1)² +(k+1)
(2k² + 4k + 2) + (k+ 1) = 2 (k+1)² + (k+1)
2(k + 1)² + (k + 1) = 2 (k+ 1)² + (k + 1)
ruas kiri = ruas kanan
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