Question

Cum calculez (3+6+9+...+30) - (2+4+6+...+20)?

Answer 1

1+2+3+....+n= n(n+1) /2
3( 1+2+...+10 )          -           2 ( 1+2+3+ ..................+10) = 
avem suma de 10 termeni
3·10 ( 10+1) /2             - 2 · 10 ( 10+1 )  / 2= 
=3· 10· 11 /2 - 2·10·11 /2 = 5·33  -  5· 22 = 5 · 11=55

Answer 2

3+6+9+...+30
pas=3
nr de termeni =(30-3):3+1=27:3+1=9+1=10
suma=(3+30)x10:2=33x10:2=330:2=165

2+4+6+...+20
pas=2
nr de termeni =(20-2) :2+1=18:2+1=9+1=10
suma=(20+2)x10:2=22x10:2=220:2=110

165-110=55