A= 22 + 24 + 26 + 28 +...... 22012
B= 3 - 32 + 33 - 34 + 35 - 36 + ..... - 32012
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1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37
=(1+37)x37:2
=703
\(a,2^2=4,2^3=8,2^4=16,2^5=32,2^6=64,2^7=128,2^8=256,2^9=512,2^{10}=1024\)
\(b,3^2=9,3^3=27,3^4=81,3^5=243\)
\(c,4^2=16,4^3=64,4^4=256\)
\(d,5^2=25,5^3=125,5^4=625\)
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50=1275
\(A=2^2+2^4+2^6+.....+2^{2012}\)
\(\Rightarrow2^2A=2^4+2^6+2^8+.....+2^{2014}\)
\(\Rightarrow4A-A=\left(2^4+2^6+....+2^{2014}\right)-\left(2^2+2^4+....+2^{2012}\right)\)
\(\Rightarrow3A=2^{2014}-2^2\)
\(\Rightarrow A=\frac{2^{2014}-2^2}{3}\)
Ta có: A= 22 + 24 + 26 + 28 +...... 22012
=> 22A = 24 + 26 + 28 +...... 22014
=> 4A - A = 22014 - 22
=> 3A =
B= 3 - 32 + 33 - 34 + 35 - 36 + ..... - 32012