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83+90+97+.........783
calculati cu suma lui gauss


Răspuns :

pasul 90-83=7
nr termeni  (783-83):7+1=100+1=101
83+90+97+.........783=(76+7)+(76+14)+(76+21)+.........(76+707)
=76×101+7+14+21+...+707=
=76×101+7×(1+2+3+...+101)=
=7676+7×101×102:2=
=7676+707×51=
=7676+36057=43733