Tính nhanh : A = 1/8 + 1/56 + 1/140 + 1/260 + 1/416
Những câu hỏi liên quan
Tính nhanh:
a)1/3+1/15+1/35+...1/195
b)6/8+6/56+6/140+...6/416
c)1/10+1/15+1/21+...1/66
a)\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{195}\)
Đặt \(C=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{66}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{132}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{11.12}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{12}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{4}+\left(-\frac{1}{5}+\frac{1}{5}\right)+\left(-\frac{1}{6}+\frac{1}{6}\right)+...+\left(-\frac{1}{11}+\frac{1}{11}\right)-\frac{1}{12}\)\(\Rightarrow\frac{1}{2}C=\frac{1}{4}+0+0+...+0-\frac{1}{12}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{4}-\frac{1}{12}\)
\(\Rightarrow\frac{1}{2}C=\frac{3}{12}-\frac{1}{12}\)
\(\Rightarrow\frac{1}{2}C=\frac{2}{12}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{6}\)
\(\Rightarrow C=\frac{1}{6}:\frac{1}{2}\)
\(\Rightarrow C=\frac{1}{6}\cdot2\)
\(\Rightarrow C=\frac{2}{6}=\frac{1}{3}\)
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Tính nhanh
a)A = 1 + 1/2 +1/4 + .......+ 1/2^99 +1/2^100+1/2^100
b) 12/56 + 12/140+12/260 +.....+ 12/1400
Tính nhanh :
a)13 – 12 + 11 + 10 – 9 + 8 – 7 – 6 + 5 – 4 + 3 + 2 – 1
b) 10/56 + 10/140 + 10/260 + ... + 10/2400
c) 1/1. 2. 3 + 1/2. 3. 4 + 1/3. 4. 5 + ... + 1/18. 19. 20
tính E=1/56+1/140+1/260+..+1/1400
Có : 2E = 1/28 + 1/70 + ..... + 1/700
= 1/4.7 + 1/7.10 + ..... + 1/25.28
6E = 3/4.7 + 3/7.10 + ..... + 3/25.28
= 1/4-1/7+1/7-1/10+.....+1/25-1/28
= 1/4-1/28 = 3/14
=> E = 1/28
Tk mk nha
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Tính nhanh: a.(1-1/2)(1-1/3)(1-1/4)...(1-1/100)
b. 10/56+10/140+10/260+.....+10/1400
Các bạn giải giùm mình nhanh nhanh được k? Mình đang cần gấp
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Tính tổng
A= 1/25x27 +1/27x29 +.............+1/73x75
B=15/ 90x94 + 15/94x98 +...............+15/146x150
C=10/56 + 10/140 + 10/260 +.................+10/1400
*** Bạn nào nhanh nhất mình Tick cho nha
\(A=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\\ A=\frac{1}{75}\)
\(B=\frac{15}{90.94}+\frac{15}{94.98}+...+\frac{15}{146+150}=\frac{1}{4}\left(\frac{15}{90}-\frac{15}{94}+\frac{15}{94}-\frac{15}{98}+...+\frac{15}{146}-\frac{15}{150}\right)\)
\(B=\frac{1}{4}\left(\frac{15}{90}-\frac{15}{150}\right)=\frac{1}{60}\)
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Đề Bài: Tính:
a) B bằng 1/6+ 1/12+ 1/20+ 1/42+ 1/56+ 1/72+ 1/90
b) C bằng 10/56+ 10/140+ 10/260+...+ 10/1400
10/56+10/140+10/260+10/416+10/608 = ?
\(\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+\frac{5}{208}+\frac{5}{304}=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\right)\)
\(=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{16}-\frac{1}{19}\right)=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{19}\right)\)
\(=\frac{5}{3}.\frac{15}{74}=\frac{25}{74}\)
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3^56+3^140+3^260+3^416+.....+3^3608