[tex]~[/tex]
1² + 2² + 3² + ... + 23² = ...
Jawaban:
1² + 2² + 3² + ... + 23² = 4.324
Penjelasan dengan langkah-langkah:
soal :
1² + 2² + 3² + ... + 23²
[tex]________________[/tex]
diketahui
1² + 2² + 3² + ... + n² = [tex]\sf \frac{n(n+1)(2n+1)}{6}\\[/tex]
penyelesaian
1² + 2² + 3² + ... + 23²
[tex] = \sf \frac{23(23 + 1)(2(23) + 1)}{6} \\ [/tex]
[tex] = \sf \frac{23( \cancel{24} \: _ \red4)(46 + 1)}{ \cancel6} \\ [/tex]
[tex] = \sf 23(4) \times 47[/tex]
[tex] = \sf 92 \times 47[/tex]
[tex] = \sf 4.324[/tex]
[tex]________________[/tex]
tambahan
misal soal = 1² + 2² + 3² + ... + 6²
= 1 + 4 + 9 + 16 + 25 + 36
= 91
jika menggunakan rumus diatas :
[tex] = \sf \frac{\cancel6(6 + 1)(2(6) + 1)}{\cancel6} \\ [/tex]
[tex] = \sf 7 \times (12+1)[/tex]
[tex] = \sf 7 \times 13[/tex]
[tex] = \sf 91 \: \to[/tex] terbukti
n → 23
Maka :
( n ( n + 1 ) ( 2n + 1 ) ) ÷ 6
( 23 ( 23 + 1 ) ( 2 ( 23 ) + 1 ) ÷ 6
( 23 ( 24 ) ( 46 + 1 ) ÷ 6
( 552 ( 47 ) ) ÷ 6
25.944 ÷ 6
4.324
[tex]\blue{\boxed{\blue{\boxed{\purple{\tt{\ \: \red{{ ༻ 彡 I \: Love \: Nanaz 彡 ༺ }}}}}}}}[/tex]
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