2+9+5+52+41+61+1+41+1+5=
CMR: 1/5+1/13+1/25+1/41+1/61+1/85+1/113<1/2
so sánh A=1/5+1/13+1/25+1/41+1/61+1/85+1/113 với 1/2
L = 3/21 + 3/41 - 3/61 / 9/21 + 9/41 - 9/61 - 11/35 - 11/10 - 11/23 / 2/35 - 2/10 - 2/23
g) (-457) + (-123) + 23 +237
h) 1 - 3 + 5 - 7 + ... + 41 - 43 + 45 - 47
i) 173 + (-46) + (-54) + (+27)+ (-19)
k) (-52) + 13 + 49 + (-15) + (-36) + 82
l) 3 + (-5) + 7 + (-9) + 11 + (-13) + 15 + (-17)
m) 1 + (-2) + 3 + (-4) + ... + 2001 + (-2002) + 2003
n) (-51) + (-53) + (-55) + ... + (-97) + (-99)
o) (-62) + (+1523) + (-38) + (-2523)+ (-92)
g: \(=-457+237+23-123=-220-100=-320\)
h: \(=\left(1-3\right)+\left(5-7\right)+...+\left(41-43\right)+\left(45-47\right)\)
\(=\left(-2\right)+\left(-2\right)+...+\left(-2\right)+\left(-2\right)\)
\(=-2\cdot12=-24\)
i: \(=173+27-46-54-19=200-100-19=100-19=81\)
k: \(=-52+82+49-15+13-36\)
\(=30+34-23\)
=30+11
=41
l: \(=\left(3-5\right)+\left(7-9\right)+\left(11-13\right)+\left(15-17\right)\)
\(=\left(-2\right)+\left(-2\right)+\left(-2\right)+\left(-2\right)\)
=-8
m: \(=\left(1-2\right)+\left(3-4\right)+...+\left(2001-2002\right)+2003\)
\(=2003-1-1-...-1\)
\(=2003-1001=1002\)
n:Số số hạng là:
\(\left[\left(-51\right)-\left(-99\right)\right]:1+1=49\left(số\right)\)
Tổng là \(\left(-51-99\right)\cdot\dfrac{49}{2}=-3675\)
o: \(=-62-38+1523-2523-92\)
\(=-100+1000-92=900-92=808\)
( 1+ 1/31+1/41+1/51) x( 1/31+1/41+1/51+1/61)- ( 1+1/31+1/41+1/51+1/61)x(1/31+1/41+1/51)=…
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+51+52+53+54+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70=?
1- ( 1/5 +1/13+1/25+1/41+1/61+1/85+1/113)
So sánh với 1/2.
chung minh rang:
1/5+1/13+1/25+1/41+1/61+1/85+1/113<1/2
1/5+1/13+1/25+1/41+1/61+1/85+1/113
=1/5+(1/13+1/25+1/41)+(1/85+1/61+1/113)<15+1/12+1/12+1/12+1/60+1/60+1/60
..............................................................<1/5+1/4+1/20
..............................................................<4/20+5/20+1/20
..............................................................<1/2