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Calculați următoarele sume:
F)15+16+17+...+70
I)317+318+319+...+400




Dau coroana!!


Răspuns :

F)
1+2+...+70=71x70:2=71x35=2485
1+2+...+14=15x14:2=15x7=105

=> 15+16+...+70=2485-105=2380

I)
1+2+...+400=401x400:2=401x200=80200
1+2+...+316=317x316:2=317x158=50086

=> 317+318+...+400=80200-50086=30114

15+16+17+...+70=

=1+2+3+...+14+15+16+17+...+70-(1+2+3+...+14)=

=70×71:2-14×15:2=

=4970:2-210:2=

=2485-105=

=2380

317+318+319+...+400=

=1+2+3+...+316+317+318+319+...+400-(1+2+3+...+316)=

=400×401:2-316×317:2=

=80200-50086=

=30114