Question

calculati sumele a)2+4+6+....+2014

Answer 1

a)2+4+6+...+2014
Observam ca avem numere pare,dam factor comun pe 2 pentru a forma o suma Gauss.

Vom avea:2+4+6+...+2014
=>2(1+2+3+...+107)

Aplicam formula [n(n+1)]/2:
2(1+2+3+...+107)
=>2[107+(107*108)]/2
=>2[107+(107*54)]
=>2(107+5778)
=>2*5885
=>11770


b)2^1+2^2+2^3+....+2^2014
Inmultim cu 2 si obtinem:
2S=2^1+2^2+2^3+...+2^2013
2S-S=2^2013-2^1
S=2^2013

Formula:a^0+a^1+a^2+...a^n=[a^(n+1)-1]/a-1.