Question

4) Calculați următoarele sume:
a) 1+2+3+...+30;
b) 2 +3 +4 + ... + 30;
c) 9+10+11+ ... + 30.​

Answer 1

Răspuns:

1+2+3+...+30=(1+30)·30:2=31·15=465

__________

2+3+4+...+30=(2+30)·29:2=29·16=464

________

30-9+1=22 numarul de termeni

9+10+11+...+30=(9+30)·22:2=39·11=429

Answer 2

a) 1+2+3+...+30=

=30×31/2=

=15×31=465

b) 2+3+4+...+30=

=1+2+3+...+30-1=

=30×31/2-1=

=15×31-1=

=465-1=464

c) 9+10+11+...+30=

=(1+2+3+...+30)-(1+2+3+...+8)=

=30×31/2-8×9/2=

=15×31-4×9=

=465-36=429