Question

Calculati sumele
a) 1+2+3+...+2006
b) 2+4+6+...+2006
c) 1+3+5+...+2005

Answer 1

Voi scrie in LaText,te voi ruga sa dai refresh la pagina daca nu iti apare rezolvarea,rezolvarea e mai jos: [tex]a)1+2+3+...+2006\\ Suma~Gauss,aplicam~formula:[n(1+n)]:2\\ =\ \textgreater \ S_n=(2006*2007):2\\ S_n=2013021\\\\ b)2+4+6+...+2006\\ Aici,pentru~a~forma~o~Suma~Gauss,dam~intai~factor\\ comun~pe~2~si~avem:\\ 2(1+2+3+...+1003)\\ Avem~o~Suma~Gauss~aplicam~formula[n(1+n)]:2\\ =\ \textgreater \ S_n=2*(1003*1004):2\\ S_n= 1007012[/tex] [tex]c)1+3+5+...+2005\\ Numerele~sunt~impare~asa~ca~folosim~formula:n*n=n^2\\ =\ \textgreater \ S_n=2005*2005\ \textless \ =\ \textgreater \ 2005^2\\ S_n= 4020025 [/tex]