2. a) (7/10+1/4+2³/40)*(7/2-3/8)*(1-2/3)²=
(7/10+1/4+2³/5*2²)*25/8*(1/3)²=
(7/10+1/4+1/5)*25/8*1/9=
23/20*25/8*1/9=
23/4*5/8*1/9=115/288 ( sau 0,399306 )
b)[tex] 20^{8}/21^{3} * 14^{5}/45^{6} * 189^{4}/140^{3} : 2^{6}/5^{6 [/tex] *3³/2^4*7^3*10^5=
5^8(2^2)^8/7^3*3^3*7^5*2^5/5^6*(3^2)^6 *7^4*(3^3)^4/20^3*7^3*[tex] 5^{6} [/tex]/[tex] 2^{6} [/tex]*[tex] 3^{3} [/tex]/[tex] 2^{4} *7^3*5^5*2^5[/tex]=
[tex]5^8*2^16/7^3*3^3 *7^5*2^5 * 7^4/7^3*(2^2)^3*5^3*1/2^6 *3^3/2^4*7^3*5^5*2^5[/tex]=
2^10*7*1/2^6*1/2^4*7=
2^4*1/2^4=1
3.a)1/n-1/n-k=k/n(n-k)= 1/n-1/n+k=n+k/n(n+k)-n/n(n-k)=n+k-n/n(n+k)=k/n(n+k)
b) 4/1*5+4/5*9+4/9*13+.........+4/2004*2008=
= 1 / n · ( n + 4) = 1 / 4 · [ 1 /n - 1 / ( n +1) =4 / 1· 5 = 4 · 1 /4 [ 1 /1 - 1/ = 4/4 · [ 1 /1 - 1 / 5 ] = 1 - 1 / 5
=4 / 5·9 = 4 / 4 · [ 1 / 5 -1 / 9 ] = 1 / 5 - 1 / 9
=4 / 9 · 13 = 4 / 4 · [ 1 / 9 - 1 /13 ] = 1 / 9 - 1 /13
=4 / 2004·2008 = 4 / 4 · [ 1 / 2004 - 1 /2008 ] = 1 /2004 - 1 / 2008
=1 - 1 /2008 = [ 2008 - 1 ] / 2008
= 2007 / 2008
1. la toate fractiile numitorul este 1440
