Question

Bantuannya nomor 2, pakai cara

Answer 1

Verified answer

Bab Eksponensial
Matematika SMA Kelas X

1 + 2 + 3 + ... + n = ?

b = U2 - U1
b = 2 - 1
b = 1

Sn = n/2 . (a + Un)
Sn = n/2 . (1 + n)

◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎

1² + 2² + 3² + ...... + n² = 1/6 . n (n + 1) (2n + 1)

◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎

(1 + 2 + 3 + 4 + ..... + n)^3 / (1² + 2² + 3² + .... + n²)²
= (n/2 . (n + 1))^3 / (1/6 . n . (n + 1) . (2n + 1))²
= (1/8 . n^3 . (n + 1)^3) / (1/36 . n² . (n + 1)² . (2n + 1)²)

◎◎ n^3 : n² = n
◎◎ (n + 1)^3 : (n + 1)² = n + 1

= 36/8 . n . (n + 1) / (2n + 1)²
= 9/2 . (n² + n)/(4n² + 4n + 1)
= (9n² + 9n)/(8n² + 8n + 2)

✩✩ A ✩✩