Sigma notasie met 3 sigmas

Sigma notasie met 3 sigmas

by Reynard du Toit -
Number of replies: 1

As stack space sum with k equals 1 below and 6 on top open parentheses x minus 3 k close parentheses equals sum from k equals 1 to 9 of open parentheses x minus 3 k close parentheses space bewys space dat stack space sum with k equals 1 below and 15 on top open parentheses x minus 3 k close parentheses equals 0

In reply to Reynard du Toit

Re: Sigma notasie met 3 sigmas

by Marna Zuhlsdorff -
Hi Reynard

Daar is drie stappe wat jy by ELKE sigma moet doen: werk die eerste drie terme uit, maak 'n inligtingslysie en vervang dit dan in die regte formule in - as jy DIT dan dan kan jy enige sigma som doen!

Hier is my oplossing en ek het 'n video by die ander sigma notasies bygesit - click hier - baie dankie dis regtig 'n goeie voorbeeld!
As sum from k equals 1 to 6 of open parentheses x minus 3 k close parentheses equals sum from k equals 1 to 9 of open parentheses x minus 3 k close parentheses space bewys space dat sum from k equals 1 to 15 of open parentheses x minus 3 k close parentheses equals 0

table row cell sum from k equals 1 to 6 of open parentheses x minus 3 k close parentheses end cell row cell T subscript 1 equals x minus 3 open parentheses 1 close parentheses equals x minus 3 end cell row cell T subscript 2 equals x minus 3 open parentheses 2 close parentheses equals x minus 6 end cell row cell T subscript 3 equals x minus 3 open parentheses 3 close parentheses equals x minus 9 end cell row blank row cell a equals x minus 3 end cell row cell d equals T subscript 2 minus T subscript 1 end cell row cell equals open parentheses x minus 6 close parentheses minus open parentheses x minus 3 close parentheses end cell row cell equals x minus 6 minus x plus 3 end cell row cell equals negative 3 end cell row cell n equals 6 minus 1 plus 1 equals 6 end cell row cell S subscript 6 equals ? end cell row blank row cell S subscript n equals n over 2 open square brackets 2 a plus open parentheses n minus 1 close parentheses d close square brackets end cell row cell S subscript 6 equals 6 over 2 open square brackets 2 open parentheses x minus 3 close parentheses plus open parentheses 6 minus 1 close parentheses open parentheses negative 3 close parentheses close square brackets end cell row cell equals 3 open square brackets 2 x minus 6 minus 15 close square brackets end cell row cell equals 3 open square brackets 2 x minus 21 close square brackets end cell row cell equals 6 x minus 63 end cell row cell therefore bold sum from bold k bold equals bold 1 to bold 6 of begin bold style left parenthesis x minus 3 k right parenthesis end style bold equals bold 6 bold italic x bold minus bold 63 end cell end table

table row cell sum from k equals 1 to 9 of open parentheses x minus 3 k close parentheses end cell row cell T subscript 1 equals x minus 3 open parentheses 1 close parentheses equals x minus 3 end cell row cell T subscript 2 equals x minus 3 open parentheses 2 close parentheses equals x minus 6 end cell row cell T subscript 3 equals x minus 3 open parentheses 3 close parentheses equals x minus 9 end cell row blank row cell a equals x minus 3 end cell row cell d equals T subscript 2 minus T subscript 1 end cell row cell equals open parentheses x minus 6 close parentheses minus open parentheses x minus 3 close parentheses end cell row cell equals x minus 6 minus x plus 3 end cell row cell equals negative 3 end cell row cell n equals 9 minus 1 plus 1 equals 9 end cell row cell S subscript 9 equals ? end cell row blank row cell S subscript n equals n over 2 open square brackets 2 a plus open parentheses n minus 1 close parentheses d close square brackets end cell row cell S subscript 9 equals 9 over 2 open square brackets 2 open parentheses x minus 3 close parentheses plus open parentheses 9 minus 1 close parentheses open parentheses negative 3 close parentheses close square brackets end cell row cell equals 9 over 2 open square brackets 2 x minus 6 minus 24 close square brackets end cell row cell equals 9 over 2 open square brackets 2 x minus 30 close square brackets end cell row cell equals 9 x minus 135 end cell row cell bold therefore bold sum from bold k bold equals bold 1 to bold 9 of begin bold style left parenthesis x minus 3 k right parenthesis end style bold equals bold 9 bold italic x bold minus bold 135 end cell end table

table row cell sum from k equals 1 to 6 of open parentheses x minus 3 k close parentheses equals sum from k equals 1 to 9 of open parentheses x minus 3 k close parentheses end cell row cell 6 x minus 63 equals 9 x minus 135 end cell row cell negative 63 plus 135 equals 9 x minus 6 x end cell row cell 72 equals 3 x end cell row cell bold italic x bold equals bold 24 end cell end table


table row cell sum from k equals 1 to 15 of open parentheses bold italic x minus 3 k close parentheses equals 0 end cell row cell sum from k equals 1 to 15 of open parentheses bold 24 minus 3 k close parentheses equals 0 end cell row cell T subscript 1 equals 24 minus 3 open parentheses 1 close parentheses equals 21 end cell row cell T subscript 2 equals 24 minus 3 open parentheses 2 close parentheses equals 18 end cell row cell T subscript 3 equals 24 minus 3 open parentheses 3 close parentheses equals 15 end cell row blank row cell a equals 21 end cell row cell d equals T subscript 2 minus T subscript 1 end cell row cell equals 18 minus 21 end cell row cell equals negative 3 end cell row cell n equals 15 minus 1 plus 1 equals 15 end cell row cell S subscript 15 equals ? end cell row blank row blank row cell L K equals S subscript n equals n over 2 open square brackets 2 a plus open parentheses n minus 1 close parentheses d close square brackets end cell row cell S subscript 15 equals 15 over 2 open square brackets 2 open parentheses 21 close parentheses plus open parentheses 15 minus 1 close parentheses open parentheses negative 3 close parentheses close square brackets end cell row cell equals 0 end cell row cell equals R K end cell end table