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.
mohon dikerjakan dengan cara.

Answer 1

A.
Beda = 2
U1 = 1
Un = 99
1 + (n - 1) . 2 = 99
1 + 2n - 2 = 99
2n - 1 = 99
2n = 100
n = 50

Berarti Sn = 50/2 [1 + 99]
Sn = 25 . 100
Sn = 2500 (total penjumlahan)

B.
1 - 2 + 3 - 4 + ... + 99 - 100
= (1 + 3 + 5 + ... + 99) - (2 + 4 + 6 + ... + 100)
= ( (1-2) + (3-4) + (5 - 6) + ... (99 - 100))
=( -1 + -1 + -1 ... + -1) sebanyak 50 kali,
berarti  = -1 x 50 = -50

C. -100 - 99 - 98 - 97 - ... + 0 + 1 + ... + 50
b = 1
U1 = -100
Un = 50
-100 + (n - 1) . 1 = 50
-100+ n - 1 = 50
n - 101 = 50
n = 151

Jumlah = 151/2 [-100 + 50] = - 3775