tính nhanh
A=3/2+7/6+13/12+...+9901/9900
K
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TC
10 tháng 7 2020
Ta có:
\(A=\frac{3}{2}+\frac{7}{6}+\frac{13}{12}+...+\frac{9901}{9900}\)
\(A=1+\frac{1}{2}+1+\frac{1}{6}+1+\frac{1}{12}+...+1+\frac{1}{9900}\)\(A=1+1+1+...+1(51c/s)+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\)
\(A=51+\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)
\(A=51+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=51+1-\frac{1}{100}\)
\(A=52-\frac{1}{100}\)
\(A=\frac{5199}{100}\)
Cái đoạn 1+1+1+...+1 ( 51 c/s) số tớ ko thể giải thích trên máy tính đc nên bn tự suy nghĩ nhé:)))
VP
2 tháng 11
A= 3/2+7/6+...+9901/9900
A=1+1/2+1+1/6+1+1/12+...+1/9900
A=(1+1+1+...+1)+(1/2+1/6+1/12+...+1/9900)
A=(1+1+1+...+1)+(1/1x2+1/2x3+1/3x4+...+1/99x100)
A=(1+1+1+...+1)+(1/1-1/2+1/2-1/3+1/3-1/4+1/4-...-1/99+1/99-1/100)
A=99+(1/1-1/100)
A=99+99/100
A=9999/100
A=9900/100+99
KL
2
3 tháng 4 2015
A=3/2+13/12+31/30+...+9901/9900
= 1+1/2+1+1/12+1+1/30+...+1+1/9900
=1+1+1+...+1+1(50 cs)+1/2+1/12+1/30+...+1/9900
=50+1/2+1/12+1/30+...+1/9900
B=5/6+19/20+41/42+...+10099/10100
=(1-1/6)+(1-1/20)+(1-1/42)+...+(1-1/10100)
=1+1+...+1(50cs)-1/6-1/20-1/42-...-1/10100
A-B=(50+1/2+1/12+1/30+...+1/9900)-(50-1/6-1/20-1/42-...-1/10100)
=1/2+1/6+1/12+1/20+...+1/9900+1/10100
=1/1.2+1/2.3+1/3.4+1/4.5+...+1/99.100+1/100.101
=1-1/2+1/2-1/3+1/3-1/4+1/4-...+1/99-1/100+1/100-1/101
=1-1/101
=100/101
11 tháng 5 2015
\(A=\frac{7}{6}+\frac{13}{12}+\frac{21}{20}+...+\frac{9901}{9900}=\left(1+\frac{1}{2.3}\right)+\left(1+\frac{1}{3.4}\right)+\left(1+\frac{1}{4.5}\right)+...+\left(1+\frac{1}{99.100}\right)\)\(=\left(1+1+1+...+1\right)+\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\right)\)
\(=98+\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\right)=98+\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(=98+\frac{49}{100}=98\frac{49}{100}\)
XS
0
7 tháng 8 2015
a) \(\frac{13}{7}-\frac{1}{2}\times\frac{13}{7}+\frac{3}{2}\times\frac{13}{7}\)
\(=\frac{13}{7}\times\left(1-\frac{1}{2}+\frac{3}{2}\right)\)
\(=\frac{13}{7}\times2\)
\(=\frac{26}{7}\)
b) \(\frac{1}{15}\times\left(\frac{3}{7}+\frac{5}{19}\right)+\frac{3}{7}\times\left(\frac{5}{19}-\frac{1}{15}\right)\)
\(=\frac{1}{15}\times\frac{3}{7}+\frac{1}{15}\times\frac{5}{19}+\frac{3}{7}\times\frac{5}{19}-\frac{3}{7}\times\frac{1}{15}\)
\(=\frac{5}{19}\times\left(\frac{1}{15}+\frac{3}{7}\right)\)
\(=\frac{5}{19}\times\frac{52}{105}\)
\(=\frac{52}{399}\)
c) \(\frac{5}{6}+\frac{5}{12}+\frac{5}{20}+\frac{5}{30}+...+\frac{5}{9900}\)
\(=5\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{99\times100}\right)\)
\(=5\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=5\times\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(=5\times\frac{49}{100}\)
\(=\frac{49}{20}\)
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