Question

Calculati:
$\sqrt{\frac{6}{5} +\frac{7}{10}+\frac{8}{15} +... +\frac{85}{400} -(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{80} ) }$
As vrea si o explicatie ,va rog

Answer 1

e corect ..dar nu e riguros

ar fi trebuit gasita formula pt termenul general si demonstrata prin inductie

Answer 2

6/5+7/10+8/15+…+85/400 – (1+1/2+1/3+….+1/80)=

=6/(1•5)+7/(2•5)+8/(3•5)+…+85/(80•5) – (1+1/2+1/3+….+1/80)

=(1/1+1/5)+(1/2+1/5)+(1/3+1/5)+…+(1/80+1/5) – (1+1/2+1/3+….+1/80)

=80•1/5+(1/1+1/2+1/3+…+1/80) – (1+1/2+1/3+….+1/80)

=80/5=16

√16=4