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\(\frac{5}{15}+\frac{3}{12}+\frac{4}{20}+\frac{18}{27}+\frac{12}{16}+\frac{30}{25}\)
\(=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}\)
\(=\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{3}{4}\right)+\left(\frac{1}{5}+\frac{4}{5}\right)\)
\(=1+1+1\)
\(=3\)
\(\frac{5}{15}+\frac{3}{15}+\frac{4}{20}+\frac{18}{27}+\frac{12}{16}+\frac{20}{25}\\ =\frac{1}{3}+\frac{1}{5}+\frac{1}{5}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}\\ \)
\(=\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{5}+\frac{1}{5}+\frac{4}{5}\right)+\frac{3}{4}\\ =1+\frac{5}{6}+\frac{3}{4}=2\frac{7}{12}=\frac{31}{12}\)
#Châu's ngốc
\(\dfrac{5}{15}+\dfrac{3}{12}+\dfrac{2}{10}+\dfrac{18}{27}+\dfrac{12}{16}+\dfrac{20}{25}\)
\(=\dfrac{1}{3}+\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{3}{4}+\dfrac{1}{5}+\dfrac{4}{5}\)
=3
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20
=(20+1)+(2+19)+...+(10+11) có 10 cặp số
=21+21+..+21 Có 10 số hạng
=21 x 10
=210
Rút gọn ta có:
\(\frac{3}{4}-\frac{4}{5}+\frac{1}{4}-\frac{1}{5}\)
=\(\left(\frac{3}{4}+\frac{1}{4}\right)-\left(\frac{4}{5}+\frac{1}{5}\right)\)
=1-1=0
\(32^{12}:16^{12}=32:16^{16}\)
\(=2^{12}\)
Nếu muốn đổi \(2^{12}\)thì chỉ cần lấy 12 lần số 2 nhân với nhau bằng 4096
1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90
1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90
9 – (1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
9 – [1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)+1/(9x10)]
9 – ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)
9 – (1 – 1/10) = 9 – 9/10 = 81/10
