Question

1+6+11+....+301=? SI 1+4+7+...+154=?
Care este regula de rezolvare a acestor tipuri de exercitii?

Answer 1

trebuie sa la găsesti factorul comun

Answer 2

1+6+11+....+301=?
6-1=5
nr termeni =(301-1) :5+1=300:5+1=61
1+6+11+....+301=1+(1+5)+(1+10)+....+(1+300)=
=1×61 +5+10+...+300=61 +5(1+2+...+60)=61 +5×60×61/2=61+9150=9211

1+4+7+...+154=
4-1=3
nr termeni =(154-1) :3+1=153:3+1=51+1=52
1+4+7+...+154=1+(1+3)+(1+6)+...+(1+153)=1×52+3+6+...+153=
=52+3(1+2+3+....+51)=52+3×51×52/2=52+3978=4030