6.
se desface in
100(1/1-1/2+1/2-1/3+.......+1/99-1/100)=100(1/1-1/100)=100(100-1)/100=100.99/100=99 (e)
7.
scriem numerele in baza 10
1/(10a+a) +1/(10b+b)=1/11a +1/11b= aducem la acelasi numitor
(a+b)/11ab
stiind ca :
1/a+1/b=5/6 ⇒(a+b)/ab=5/6 ⇒a+b=5ab/6 ,inlocuind
(a+b)/11ab=55ab/6 ·11ab=55/66=5/6 (e)