Tuliskan dalam bentuk notasi sigma

a) 2 + 5 + 8 + .... + 74 = ₁Σ²⁵ (3n - 1)
Cara :
selalu bertambah 3 sehingga
Un = 3n + c
U₁ = 2
3(1) + c = 2
c = -1
Un = 3n - 1
Un = 74
3n - 1 = 74
3n = 75
n = 25

b) -1 - 5 - 9 - .... - 41 = ₁Σ¹¹ (-4n + 3)
Cara :
selalu berkurang 4 maka Un = -4n + c
U₁ = -1
-4(1) + c = -1
c = 3
Un = -4n + 3
Un = -41
-4n + 3 = -41
-4n = -44
n = 11

c) 2 + 3/2 + 4/3 + .... + 21/20
= 2/1 + 3/2 + 4/3 + ... + 21/20
= (1 + 1)/1 + (2 + 1)/2 + (3 + 1)/2 + ... + (20 + 1)/20
= ₁Σ²⁰ (n + 1)/n

d) 2 - 4 + 6 - ..... - 56
= 2.1 - 2.2 + 2.3 - ... - 2.28
= ₁Σ²⁸ (-1)ⁿ⁻¹ . 2n


e) 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
= (1/2)² + (1/2)³ + (1/2)⁴ + (1/2)⁵ + (1/2)⁶ + (1/2)⁷
= ₁Σ⁶ (1/2)ⁿ⁺¹

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Kelas : 11
Mapel : Matematika
Kategori : Induksi Matematika
Kata Kunci : notasi sigma
Kode : 11.2.1 (Matematika Bab 1. Induksi Matematika)