Question

DAU COROANA!!!!Calculați suma nr. naturale pare de forma 2xy

Answer 1

Numerele naturale pare de forma 2xy sunt: 200, 202, 204, ... , 298

Suma lor este:

200+202+204+...+298=

=2×100+2×101+2×102+...+2×149=

=2(100+101+102+...+149)=

=2[1+2+3+...+99+100+101+...+149-(1+2+3+...+99)]=

$=2*(\frac{149*150}{2}-\frac{99*100}{2})=$

$=2*(\frac{149*150-99*100}{2})=$

=149×150-99×100=

=22.350-9.900=

=12.450

Answer 2

S=200+202+204+206+.................298
numarul de termeni:
N=(298-200)/2 +1=50
S=(298+200)N/2=498*50/2=12450

am folosit formulele generale:
N=(ultimul termen - primul termen)/(diferenta dintre doi termeni consecutivi) + 1
S=(primul termen + ultimul termen)N/2