-1+2-3+4-5+6-7+8-…+100 tlong di jwb yh

Materi Barisan

Kelompokkan secara asosiatif
(-1 + 2) + (-3 + 4) + … + (-99 + 100)
= 1 + 1 + … + 1 (sebanyak 50)
= 1 × 50 = 50

Deret Bolak-Balik.

-1 + 2 – 3 + 4 – 5 + 6 – 7 + 8 – … + 100
= -(1 + 3 + 5 + 7 + … + 99) + 2(1 + 2 + 3 + 4 + … + 50)

Tinjau deret 1 + 3 + 5 + 7 + … + 99.
Un = a + (n – 1)b
n = (Un – a) / b + 1
   = (99 – 1) / 2 + 1 = 50
Sn = n/2 [2a + (n – 1)b]
S₅₀ = 50/2 [2(1) + (50 – 1)(2)] = 2500

Tinjau deret 1 + 2 + 3 + 4 + … + 50.
Un = a + (n – 1)b
n = (Un – a) / b + 1
   = (50 – 1) / 1 + 1 = 50
Sn = n/2 [2a + (n – 1)b]
S₅₀ = 50/2 [2(1) + (50 – 1)(1)] = 1275

Jadi:
-1 + 2 – 3 + 4 – 5 + 6 – 7 + 8 – … + 100
= -(1 + 3 + 5 + 7 + … + 99) + 2(1 + 2 + 3 + 4 + … + 50)
= -2500 + 2(1275)
= 50