Sigma 5x² + 6 dengan x dimulai dari 2 hingga 5. Maka nilainya adalah...

Sigma 5x² + 6 dengan x dimulai dari 2 hingga 5. Maka nilainya adalah…

» Notasi Sigma

$displaystyle rm sum_{x= 2}^5(5 {x}^{2} + 6)$

$displaystyle rm = sum_{x= 2 - 1}^{5 - 1}(5 {(x + 1)}^{2} + 6)$

$displaystyle rm = sum_{x= 2 - 1}^{5 - 1}(5 {( {x}^{2} + 2x + 1)}+ 6)$

$displaystyle rm = sum_{x = 2 - 1}^{5 - 1}(5 { {x}^{2} + 10x + 5}+ 6)$

$displaystyle rm = sum_{x = 1}^{4}(5 {x}^{2} + 10x + 11)$

$displaystyle rm = sum_{x = 1}^{4}(5 {x}^{2} )+ sum_{x = 1}^{4}10x + sum_{x = 1}^{4}(11)$

$displaystyle rm = ((5 {(1)}^{2}) + (5 {(2)}^{2}) + (5 {(3)}^{2}))+ (5 {(4)}^{2}) )+ sum_{x = 1}^{4}10x + sum_{x= 1}^{4}(11)$

$displaystyle rm = (5 + 20 + 45+ 80)+ sum_{x = 1}^{4}10x + sum_{x= 1}^{4}(11)$

$displaystyle rm = 150+ sum_{x = 1}^{4}10x + sum_{x= 1}^{4}(11)$

$displaystyle rm = 150+(10(1) + 10(2) + 10(3) + 10(4)) + sum_{x= 1}^{4}(11)$

$displaystyle rm = 150+(10 + 20 + 30 + 40)+ sum_{x= 1}^{4}(11)$

$displaystyle rm = 150+100+ sum_{x= 1}^{4}(11)$

$displaystyle rm = 150+100+ (4 times 11)$

$displaystyle rm = 150+100+ 44$

$displaystyle rm =250+ 44$

$boxed{ displaystyle rm =294}$

Maka :

$sf sum^{5} _{x = 2} : (5 {x}^{2} + 6) \$

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(5(2)² + 6) + (5(3)² + 6) + (5(4)² + 6) + (5(5)² + 6)

= (5(4) + 6) + (5(9) + 6) + (5(16) + 6) + (5(25) + 6)

= (20 + 6) + (45 + 6) + (80 + 6) + (125 + 6)

= 26 + 51 + 86 + 131

= 77 + 86 + 131

= 163 + 131

= 294

Koreksiii