(9-1/100)^3×(9-2/100)^3×(9-3/100)^3×...×(9-2016/100)^3= NO.3 dan 4 kalo bisa

Kelas 7 Matematika
Bab Pola Bilangan

^ = pangkat

3] (9 - 1/100)^3 . (9 - 2/100)^3 . .... . (9 - 2.016/100)^3
= (9 - 1/100)^3 . (9 - 2/100)^3 . .... . (9 - 900/100) . ... . (9 - 2016/100)
= ((900 - 1)/100)^3 . ((900 - 2)/100)^3 . ... ((900 - 900)/100)^3 . .... . ((900 - 2016)/100)^3
= (899/100)^3 . (898/100)^3 . .... . (0/100)^3 . .... . (-1.116/100)^3
= (899/100)^3 . (898/100)^3 . 0 . ... . (-1.116/100)^3
= 0

✩✩ C ✩✩

4] 1/2 + 1/6 + 1/12 + ... + 1/9.900 = ?

1/2

→ 1/(1 . 2)

1/2 + 1/6
= 3/6 + 1/6
= 4/6
= 2/3

→ 1/6 = 1/(2 . 3)

1/2 + 1/6 + 1/12
= 6/12 + 2/12 + 1/12
= 9/12
= 3/4

→ 1/12 = 1/(3 . 4)

Perhatikan polanya

1/9.900 = 1/(99 . 100)

Maka

1/2 + 1/6 + 1/12 + ... + 1/9900
= 1/(1 . 2) + 1/(2 . 3) + 1/(3 . 4) + ... + 1/(99 . 100)
= 99/100
= 0,99

✩✩ C ✩✩