Question

Tentukan hasil dari 1-2+3-4+5-6+7-8...-100

Answer 1

Ganjil
a= 1
b= 2
suku terakhir = 99
99 = 1 + (n -1)b
98 = (n-1)2
49 = n-1
n=50

Sn = 50/2 (2+(50-1)2) = 25 (2 + 98) = 2500

genap
a= 2
b= 2
suku terakhir = 100
100 = a + (n-1)b
100 = 2 + (n-1) 2
98 = 2n -2
100 = 2n
n=50

Sn = 50/2 (2+(50-1)2) = 25 (2 + 98) = 2500

maka ganjil - ( genap) = 2500 - 2500 = 0

Answer 2

Bilangan ganjil
1 + 3 + 5 + ......+ 99
a = 1
b = 2
Un = 99
n = 50 bilangan
Sn = n/2 ( a + un)
S50 = 50/2. ( 1 + 99)
       = 25 x 100
       = 2500

bilangan genap
-2 + -4 + -6 + -8....+ - 100
a = -2
b = -2
Un = - 100
n = 50 bilanan
Sn = n/2 ( a + un)
     = 50/2 ( -2 + ( -100))
     = 25. ( - 102)
     = 2550

maka jumlahnya seluruhnya 2500 + ( - 2550) = - 50