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Efectuati:
(√2-1)/√2+(√3-√2)/√6+⋯+(√9-√8)/√72


Răspuns :

(√2-1)/√2+(√3-√2)/√6+(√9-√8)/√72=
=(√2-1)/√2+(√3-√2)/√6+(3-2√2)/6√2=
=[6(√2-1)+2√3(√3-√2)+3-2√2]/6√2=
=(6√2-6+6-2√6+3-2)/6√2=
=(6√2-2√6+1)/6√2