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S= 1/44+1/45+...+1/103; aratati ca S<3/2

Răspuns :

media armonica =nr de termeni//(1/x1+1/x2+....1/xn)⇒ in cazul sumei S sunt 60 de termeni (103-43=60) S=60/44+45+46+....103. dar 44+45+...103=(44+103)*60/2=4410⇒ S=60/4410=6/441 =0,013⇒ 3/2=1,5 S<3/2