Question

1+3+5+7+.......+999=?​

Answer 1

Metoda I:

1+3+5+7+...+999 =

= 1+2+3+4+...+499

+1+2+3+...+500

= (1+2+3+...+499) + (1+2+3+...+500)

= (499•500)/2 + (500•501)/2

= 499•250 + 250•501

= 250•(499+501)

= 250•1000

= 250000

Metoda II:

1+3+5+7+...+999 =

= (2•1-1)+(2•2-1)+(2•3-1)+...+(2•500-1)

= 2•1+2•2+2•3+...+2•500 -1-1-1-...-1

{de 500 ori}

= 2•(1+2+3+...+500) - 1•500

= 2•[500•(500+1)]/2 - 500

= 500•(500+1) - 500

= 500•501 - 500

= 500•(501-1)

= 500•500

= 250000

Metoda III:

1+3+5+7+...+999 =

= (1+999)+(3+997)+(5+995)+...+(499+501)

= 1000+1000+...+1000

{de (499+1)/2 = 250 ori}

= 1000•250

= 500•500

= 250000

Answer 2

Răspuns:

Explicație pas cu pas:

S=1+3+5+7+....+999

S=1+3+4+5+7 +...(2n-1)

S =n*n

2n-1=999

2n=1000

n= 500

S= 500*500

S= 250.000

Succes !!