Question

A.|-1|+|-2|+|-3|+......+|-64|=

B.|-5|+|-10|+|-15|+...+|-250|=

C.|-2|+|-4|+|-6|+.....+|-102|=

D.|-1|+|-4|+|-7|+......+|-235|=


Ajutor!!

Answer 1

A) |-1|+|-2|+|-3|+...+|-64|=1+2+3+...+64=

=64×65/2=32×65=2080

B) |-5|+|-10|+|-15|+...+|-250|=

=5+10+15+...+250=

=5×(1+2+3+...+50)=

=5×(50×51/2)=

=5×25×51=

=6375

C) |-2|+|-4|+|-6|+...+|-102|=

=2+4+6+...+102=

=2×(1+2+3+...+51)=

=2×(51×52/2)=

=2×51×26=

=2652

D) |-1|+|-4|+|-7|+...+|-235|=

=1+4+7+.....+235=

=1+(1+3)+(1+2×3)+....+(1+78×3)=

=1+1+1+...+1+(3+2×3+...+78×3)=

(de 79 ori)

=79+(3+2×3+...+78×3)=

=79+3×(1+2+3+...+78)=

=79+3×(78×79/2)=

=79+3×39×79=

=79×(1+3×39)=

=79×(1+117)=

=79×118=

=9322