Page 233 - aljaber

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a1, a2, a3, …, an .

.Sn

Sn = a1 + a2 + + an
1, 4, 9, 16, 25, …

Sn = 12 + 22 + 32 + 42 + + n2

S1 = 12 = 1
S2 = 12 + 22 = 1 + 4 = 5
S3 = 12 + 22 + 32 = 1 + 4 + 9 = 14

(Arithmetic Series)ِ (.)

.

3 + 5 + 7 + + 23 + 25

. 3, 5, 7, …, 23, 25
.d a1, a2, a3, …, an

.a1, a1 + d, a1 + 2d, …, an − 2d, an − d, an

Sn = a1 + (a1 + d) + (a1 + 2d) + + (an − 2d) + (an − d) + an