Contoh Soal dan Pembahasan Notasi Sigma

Sebelumnya silakan memahami tentang sifat sifat notasi sigma. Adapun beberapa sifat notasi sigma bisa dibaca di : Sifat Sifat Notasi Sigma.

Tentukanlah Hasil dari Notasi sigma berikut.

1. $ \displaystyle \sum_{k=5}^{5} \,(k^5 + 7) $
2.  $ \displaystyle \sum_{k=1}^{15} \,(k + 3) $
3. $ \displaystyle \sum_{k=1001}^{1009} \,(5k + 3) $

1. $ \displaystyle \sum_{k=5}^{5} \,(k^5 + 7) $
Berdasarkan sifat (5) : $ \displaystyle \sum_{k=n}^{n} \, a_k = 0 $.
$ \begin{align} \displaystyle \sum_{k=5}^{5} \,(k^5 + 7) & = 0 \end{align} $

2. $ \displaystyle \sum_{k=1}^{15} \,(k + 3) $
Berdasarkan sifat (6) : $ \displaystyle \sum_{k=m}^{n} \, a_k = \displaystyle \sum_{k=m}^{p-1} \, a_k + \displaystyle \sum_{k=p}^{n} \, a_k $.
$ \begin{align} \displaystyle \sum_{k=1}^{15} \,(k + 3) & = \displaystyle \sum_{k=1}^{9} \,(k + 3) + \displaystyle \sum_{k=10}^{15} \,(k + 3) \end{align} $

3. $ \displaystyle \sum_{k=1001}^{1009} \,(5k + 3) $
Bedasarkan sifat (7) : $ \displaystyle \sum_{k=m}^{n} \, a_k = \displaystyle \sum_{k=m-p}^{n-p} \, a_{k+p} $.
$ \begin{align} \displaystyle \sum_{k=1001}^{1009} \,(5k + 3) & = \displaystyle \sum_{k=1001 -1000}^{1009-1000} \,[5(k + 1000) + 3] \\ & = \displaystyle \sum_{k=1}^{9} \,(5 k + 5003) \end{align} $