Răspuns:
Explicație pas cu pas:
0,3333...+0,2727...+1,2323...=1,8383...=1,(83)
1,(83) = (183-1)/99= 182/99
4,5:0,09= 14/10*100/9 = 50
50+2+2/3 = 52+2/3 = 158/3
(x+1)/x = 182/99*3/158*2607= 91
x+1 = 91x
1 = 90x ; x = 1/90
43. 1+2+3...+2010=2010*2011/2 = 1005*2011
2010-2009+2008-2007+...+4-3+2-1=
1+1+1...+1+1 = 1005; (2010/2 = 2005)
1/1*2 + 1/2*3 + ...+1/2010*2011=
1-1/2 + 1/2-1/3+...+1/2010 - 1/2011 =
1-1/2001 = 2010/2011
1005*2011/1005 = x/(1/2011)
2011 = x*2011
x = 1
