Question

Rezolvarea exercițiilor 42 si 43.Va rog!!!Dau coroana!!!​

Answer 1

Răspuns:

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Answer 2

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