Question

Tanpa menghitung satu per satu , hitunglah :

A. 1-2+3-4+5-6+7-8+ .... -100
B. -100-99-98- ... -2-1-0+1+2+ ... +48+49+50

Answer 1

A. (1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + ... + (99 - 100) = -1 x 50 = -50

B. -100 - 99 - 98 - ... - 2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50
= - 100 - 99 - ... - 49
a = -100
b = - 99 - (- 100) = 1
Un = -49
Un = a + (n - 1)b
- 49 = - 100 + (n - 1)1
- 49 = -100 + n - 1
n = 52
S₅₂ = (52/2)(2(-100) + 51(1))
= 26(-200 + 51)
= 26(-149)
= - 3874

Answer 2

A.tiap 2 suku hasilnya -1 jadi banyak suku 100/2=50
-1 dikali 100/2=-1 dikali 50=-50
b.Un=-100+(n-1)1
=-100+n-1=n-101=50
n=151
S151=151/2(-100+50)=151/2.(-50)=-3775