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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, (dengan caranya)


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

(dengan caranya)


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Mapel : Matematika
Kelas : IX SMP
Bab : Barisan dan deret

Pembahasan :
Un = 2n – 1
99 = 2n – 1
2n = 100
n = 50

1 + 3 + 5 + 7 + … + 99 = n²
1 + 3 + 5 + 7 + … + 99 = 50²
1 + 3 + 5 + 7 + … + 99 = 2500

————————————————
1 – 2 + 3 – 4 + … – 100
= -1 – 1 – 1 – 1 – … – 1
= -(1 + 1 + … + 1)
= -(100/2)
= -50

————————————————
Un = 50
a + (n – 1)b = 50
-100 + n – 1 = 50
n – 101 = 50
n = 151

-100 – 99 – 98 – … + 50
= S151
= 151/2(-100 + 50)
= 151/2(-50)
= -3775

Originally posted 2022-06-05 10:09:39.



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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, (dengan caranya)

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