HOTS Zone : Notasi Sigma

Berikut ini adalah kumpulan soal mengenai notasi sigma tipe HOTS. Jika ingin bertanya soal, silahkan gabung ke grup Facebook atau Telegram.

Tipe:

Standar SBMPTN HOTS

No. 1

Buktikan {\displaystyle\sum_{j=1}^n\left(a_j-a_{j-1}\right)=a_n-a_0}

Grup Telegram

$\begin{array}{rl}{\displaystyle \sum _{j=1}^n(a_j-a_{j-1})}& ={\displaystyle \sum _{j=1}^n\left(a_j\right)-{\displaystyle \sum _{j=1}^n\left(a_{j-1}\right)}}\\ & ={\displaystyle \sum _{j=1}^{n-1}\left(a_j\right)+a_n-{\displaystyle \sum _{j=1-1}^{n-1}\left(a_{j+1-1}\right)}}\\ & ={\displaystyle \sum _{j=1}^{n-1}\left(a_j\right)+a_n-{\displaystyle \sum _{j=0}^{n-1}\left(a_j\right)}}\\ & ={\displaystyle \sum _{j=1}^{n-1}\left(a_j\right)+a_n-(a_0+{\displaystyle \sum _{j=1}^{n-1}\left(a_j\right)})}\\ & ={\displaystyle \sum _{j=1}^{n-1}\left(a_j\right)+a_n-a_0-{\displaystyle \sum _{j=1}^{n-1}\left(a_j\right)}}\\ & =a_n-a_0\end{array}$

TERBUKTI.