1
18²+24²+40²=2²(9²+12²+20²)=2²(15²+20²)=2² * 25²=(2*25)²=50²
√(50²)=50
altfel
18²+24²+40²=324+576+16500=900+1600=2500=25*100=5² *10²=50²
√50²=50
4
1/1*2=1/1-1/2
1/2*3=1/2-1/3
......................
1/[n(n+1)]=1/n/(n+1)
atunci prima paranteza rotunda devine
1/1-1/2=1/2-1/3+1/3-1/4+....+1/43-1/44.+1/44-1/45= 1-1/45=44/45
iar a doua
1/45-1/46+1/46-1/47+1/47-1/4 +.......+1/88-1/89+1/89-1/90=1/45-1/90=2/90-1/90=1/90
iar toata expresia de sub radical
29*30(44/45-1/90)=29*30 (88/90-1/90)=29*30* (87/90)=29*87/3=29*29=29²
deci √29²=29
raspuns corect D
