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3/2+7/6+13/12+21/20+...+133/132
=1+ 1/2 + 1+ 1/6 + 1+ 1/12 + 1+ 1/20+......+ 1+ 1/132
=(1+ 1 + 1+.....+ 1) + ( 1/2+ 1/6+1/12+ 1/20+....+ 1/132)
= 11+ ( 1/1×2+ 1/2×3+1/3×4+1/4×5+.....+1/11×12)
=11+ ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/11-1/12)
=11+(1-1/12)
= 11+11/12
=143/12
3/2+7/6+13/12+21/20+...+133/132 =1+ 1/2 + 1+ 1/6 + 1+ 1/12 + 1+ 1/20+......+ 1+ 1/132 =(1+ 1 + 1+.....+ 1) + ( 1/2+ 1/6+1/12+ 1/20+....+ 1/132) = 11+ ( 1/1×2+ 1/2×3+1/3×4+1/4×5+.....+1/11×12) =11+ ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/11-1/12) =11+(1-1/12) = 11+11/12 =143/12
\(M=\frac{1}{1000}+\frac{13}{1000}+\frac{25}{1000}+\frac{37}{1000}+...+\frac{121}{1000}+\frac{133}{1000}\)
\(=\frac{1+13+25+37+...+121+133}{1000}\)
\(=\frac{804}{1000}=\frac{201}{250}\)
\(...=\dfrac{3}{2}x\left(1+\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}\right)\)
\(=\dfrac{3}{2}x\left(\dfrac{256}{256}+\dfrac{64}{256}+\dfrac{16}{256}+\dfrac{4}{256}+\dfrac{1}{256}\right)\)
\(=\dfrac{3}{2}x\dfrac{341}{256}=\dfrac{1023}{512}\)
a: Đặt A=2+4+...+82+84
Số số hạng là (84-2):2+1=42(số)
Tổng là (84+2)*42/2=1806
Đặt B=4+7+...+130+133
Số số hạng là (133-4):3+1=44(số)
Tổng là (133+4)*44/2=3014
=>C=1806/3014=903/1507
b: \(=\dfrac{18\left(123+4567+5310\right)}{132+48}=\dfrac{18\cdot10000}{180}=1000\)
M =1/1000+13/1000+25/1000+37/1000+...+121/1000+133/1000
\(M=\frac{1+13+25+...+133}{1000}\)
\(M=\frac{\left(133+1\right)\times12:2}{1000}\)
\(M=\frac{804}{1000}=0,804\)
b:3=1/2+1/4+1/8+1/16+1/32+1/64+1/128
[b:3]x2=1+1/2+1/4+1/8+1/16+1/32+1/64
[b:3]x2-[b:3]=1+1/2+1/4+1/8+1/16+1/32+1/64-1/2+1/4+1/8+1/16+1/32+1/64+1/128
b:3=1-1/128
b:3=127/128
b=127/128x3
b=381/128
B.2=\(3+\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\frac{3}{16}+\frac{3}{32}+\frac{3}{64}\)\(+\frac{3}{128}\)
B.2-B=\(\left(3+\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\frac{3}{16}+\frac{3}{32}+\frac{3}{64}+\frac{3}{128}\right)\).\(\left(\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\frac{3}{16}+\frac{3}{32}+\frac{3}{64}+\frac{3}{128}\right)\)
B=3-\(\frac{3}{128}\)
B=\(\frac{381}{128}\)
138-3+8=141+8=149
138-3*8 chu