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2014-10-21T22:43:43+03:00
  1+  2+  3+...+30
30+29+28+...+1
_______________
31+31+31+...+31=31X30/2=930/2=465.
       
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2014-10-21T23:02:22+03:00
10..1+2+3+...+30=30*31:2=465
11+22+33+...330=11(1+2+3+...33)=11*33*34:2=6171
5+10+15+...+150=5(1+2+3+...+30)=5*30*31:2=2325
11...
3+5+7+...+2003=3+(3+2*1)+(3+2*2)+...+(3+2*1000)=3+3+..+3+2(1+2+...+1000)=3*1001+2*1000*1001:2=3003+1001000=1004003
2+4+6+...+2002=2(1.2+3+...1001)=2*1001*1002:2=1003002

3+5+7+...+2003-2-4-6-...-2002=3+5+7+...+2003-(2+4+6+...+2002)=1004003-1003002=1001

12...
a. 11+22+33+44+55+66+77+88+99=11(1+2+3+..+9)=11*9*10:2=495
b. 111+222+333+...+999=111(1+2+3+...+9)=111*9*10:2=4995

13..
axb=4984
axb+2xa=5096
4984+2xa=5096
2xa=5096-4984
2xa=112
a=112:2
a=56

axb=4984 si a=56⇒b=4984:56=89

14...
892·x+18·x=9100
910·x=9100
x=9100:910
x=10

75·x+24·x=990
99·x=990
x=990:99
x=10

37·x+73·x=11100
111·x=11100
x=11100:111
x=100