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MFM
a fost răspuns

Calculati suma
S=1/(√3+2√2)+ 1/(√5+2√6) +............+1/√2n+1+2√(n²+n)
mentionez ca primul radical este peste tot numitorul .

Răspuns :

Uhaciioan
2n+1+2√(n²+n)=n+1+n+2√(n²+n)=(rad n+1 +rad n) la 2
deci 1/√2n+1+2√(n²+n)=1/rad n+1 +rad n=

rationalizam
=rad n+1 -rad n / n+1 -n =rad n+1 - rad n


inlocuind in suma obtinem
S=rad 2-rad 1+rad3-rad2 +rad 4-rad 3+......+rad n+1- rad n=
rad n+1    - 1