Tolong. Poinnya lumayan loh

Tolong. Poinnya lumayan loh

Penjelasan dengan langkah-langkah:

Beberapa Sifat Notasi Sigma yang digunakan

$Sigma^n_{i=1}k=n.k k=konstanta\\Sigma^n_{i=p}k=Sigma^n_{i=1}k-Sigma^p_{i=1}k k=konstanta\\Sigma^n_{i=1}i=frac{n(n+1)}{2} \\Sigma^n_{i=j}Ui=Sigma^n_{i=p}Ui+Sigma^{p-1}_{i=j}Ui\\Sigma^n_{i=1}Ui=Sigma^n_{i=j}Ui-Sigma^{p-1}_{i=j}Ui$

1. $Sigma^4_{k=0} (2k-4)$

$Sigma^4_{k=0} (2k-4)\\=Sigma^{4+3}_{k=0+3} (2(k-3)-4)\\=Sigma^{4+3}_{k=0+3} (2k-6-4)\$

$boxed{=Sigma^{7}_{k=3} (2k-10)}$

2. $Sigma^{50}_{i=4}(3+pi)$

$Sigma^{50}_{i=4}(3+pi)\\=Sigma^{50}_{i=4}3+Sigma^{50}_{i=4}(pi)\\=Sigma^{50}_{i=4}3+Sigma^{50}_{i=4}(pi)\\=Sigma^{50}_{i=1}3-Sigma^{3}_{i=1}3+Sigma^{50}_{i=4}(pi)\\=(50)3-3(3)+20\\=150-9+20\\boxed{=161}$

3. $Sigma^{51}_{k=4}(k-5)$

$Sigma^{51}_{k=4}(4k-5)\\=Sigma^{51-3}_{k=4-3}(4(k+3)-5)\\=Sigma^{48}_{k=1}(4k+12-5)\\=Sigma^{48}_{k=1}(4k+7)\\=4Sigma^{48}_{k=1}k+Sigma^{48}_{k=1}7\\=4(frac{(48(1+48))}{2} )+(48)7\\=4(1176)+336\\=4704+336\\boxed{=5040}$

4. $Sigma^4_{k=2}(2k-4) + Sigma^7_{k=5}(2k-4)$

$Sigma^4_{k=2}(2k-4) + Sigma^7_{k=5}(2k-4)\\=Sigma^7_{k=5}(2k-4)+Sigma^4_{k=2}(2k-4)\\=Sigma^7_{k=2}(2k-4)\\=Sigma^{7-1}_{k=2-1}(2(k+1)-4)\\=Sigma^{6}_{k=1}(2k+2-4)\=Sigma^{6}_{k=1}(2k-2)\\=2Sigma^{6}_{k=1}k-Sigma^{6}_{k=1}2\\=2(frac{6(7)}{2} )-(6).2\\=2(21)-12\\=42-12\\boxed{=30}$

Detail :

Bab : Notasi Sigma

Kata Kunci : dio.Notasi_Sigma