Page 32 - Modul Kapita Selekta Matematika-converted(1)
P. 32
Contoh 2:
Hitunglah
(a) ∑ 4 2 (b) ∑ 3 ( − 1)
=1
=1
Jawab:
(a) ∑ 4 2 = 2.1 + 2.2 + 2.3 + 2.4 = 2 + 4 + 6 + 8 = 20
=1
(b) ∑ 3 ( − 1) = (1 - 1) + (2 – 1) + (3 – 1) = 0 + 1 + 2 = 3
=1
B. Sifat-sifat Notasi Sigma
(a) ∑ = ∑
=1
=1
(b) ∑ = dengan A adalah suatu konstanta
=1
(c) ∑ = ∑ dengan A adalah suatu konstanta
=1
=1
(d) ∑ ( ± ) = ∑ ± ∑
=1
=1
=1
2
2
2
(e) ∑ ( ± ) = ∑ + 2 ∑ + ∑
=1
=1
=1
=1
(f) ∑ + ∑ = ∑
=1
= +1
=1
(g) ∑ = ∑ −1 + 1 = ∑ +1 − 1
=1
=1
=1
(h) ∑ = dengan k = 1, 2, 3, ..., n (bilangan asli)
=
Bertanya
Tugas
Buktikanlah sifat-sifat notasi sigma diatas!
Contoh 3:
Buktikan bahwa:
2
2
(a) ∑ 3 = 3 ∑
=1
=1
2
2
(b) ∑ 12 = ∑ 7 + 10 ∑ 7 + 175
=6
=1
=1
Bukti:
2
2
2
2
2
(a) ∑ 3 = 3 (1) + 3(2) + 3(3) + … + 3( )
=1
2
2
2
2
= 3(1 + 2 + 3 + ...+ n )
2
= 3∑ .... terbukti
=1
2
2
(b) ∑ 12 = ∑ 12−5 ( + 5)
=6−5
=6
2
= ∑ 7 ( + 10 + 25)
=1
2
= ∑ 7 + ∑ 7 10 + ∑ 7 25
=1
=1
=1
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