Question

Tentukan hasil dari (tanpa menghitung satu persatu)
a.1+3+5+7+9+...+99
b.1-2+3-4+5-6+7-8+...-100
c.-100-99-98-...-2-1-0+1+2+...+48+49+50
jelaskan caranya!

Answer 1

1)
a = U1 = 1
b = U2 - U1 =  2

Un = a + (n-1)b
99 = 1 + (n-1)2
99 = 1 + 2n - 2
99 = 2n - 1
2n = 100
n = 100/2
n = 50

Sn = (n/2)(a + Un)
S50 = (50/2)(a + U50)
S50 = 25(1+99)
S50 = 25(100)
S50 = 2500

2) 1-2 = -1
     3-4 = -1

     begitu seterusnya
     jadi 1-2+3-4+5-6+7-8+...-100 = -50

3) = 50/2 (-100+(-51))
    = 25 x -151
    = - 3775