tinh nhanh nang cao
1+1/3+1/6+1/12+1/24+1/48+1/80+1/160
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T
28 tháng 5 2018
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)
\(\Rightarrow3A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(\Rightarrow3A=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}\)
\(\Rightarrow3A=1+1-\frac{1}{32}\)
\(\Rightarrow3A=2-\frac{1}{32}\)
\(\Rightarrow A=\left(2-\frac{1}{32}\right):3=\frac{21}{32}\)
P/s : Đúng nha
2
0
NH
1
TN
24 tháng 4 2016
A= \(\frac{1}{3}+\frac{1}{8}+\frac{1}{15}+\frac{1}{24}+\frac{1}{35}+\frac{1}{48}+\frac{1}{63}+\frac{1}{80}\)
A= \(\frac{2}{2}.\left(\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+\frac{1}{4.6}+\frac{1}{5.7}+\frac{1}{6.8}+\frac{1}{7.9}+\frac{1}{8.10}\right)\)
A=\(\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\right)\)
\(A=\frac{1}{2}.\left(1-\frac{1}{9}+\frac{1}{2}-\frac{1}{10}\right)\)
A= tự tính
S
23 tháng 2 2017
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)
\(=\frac{1}{2}+\frac{1}{8}+\frac{1}{32}\)
\(=\frac{5}{8}+\frac{1}{32}\)
\(=\frac{21}{32}\)
LL
1
TN
8 tháng 5 2016
\(=2\left(\frac{1}{3}+\frac{1}{6}+...+\frac{1}{192}\right)\)
\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+...+\frac{1}{96}-\frac{1}{192}\right)\)
\(=2\left(1-\frac{1}{192}\right)\)
\(=2\times\frac{191}{192}\)
\(=\frac{191}{96}\)
TP
2
VD
1
1+1/3+1/6+1/12+1/48+1/80+1/160 = (1+1/3+1/6+1/12+1/24+1/48)+1/80+1/160
Tách bt thành 2 tổng:
Tổng thứ 1: A=1+1/3+1/6+1/12+1/24+1/48
2A = 2 + 2/3+1/3+1/6+1/12+1/24
A= (2+2/3+1/3+1/6+1/12+1/24)-(1+1/3+1/6+1/12+1/24+1/48)=1+2/3 - 1/48 = 79/48
1/80+1/160= 3/160
Ta có : 79/48 + 3/160 = 799/480