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AH
Akai Haruma
Giáo viên
9 tháng 11 2021
Lời giải:
$\frac{A}{2}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$
$=\frac{2-1}{1\times 2}+\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+\frac{5-4}{4\times 5}+\frac{6-5}{5\times 6}+\frac{7-6}{6\times 7}+\frac{9-8}{8\times 9}+\frac{10-9}{9\times 10}$
$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}$
$=1-\frac{1}{9}=\frac{8}{9}$
$\Rightarrow A=2\times \frac{8}{9}=\frac{16}{9}$
BN
1
H9
HT.Phong (9A5)
CTVHS
16 tháng 10 2023
\(A=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+\dfrac{1}{45}+\dfrac{1}{55}\)
\(A=2\times\dfrac{1}{2}\times\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+\dfrac{1}{45}+\dfrac{1}{55}\right)\)
\(A=2\times\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}\right)\)
\(A=2\times\left(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+...+\dfrac{1}{9\times10}+\dfrac{1}{10\times11}\right)\)
\(A=2\times\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{10}-\dfrac{1}{11}\right)\)
\(A=2\times\left(\dfrac{1}{2}-\dfrac{1}{11}\right)\)
\(A=2\times\dfrac{9}{22}\)
\(A=\dfrac{9}{11}\)
21 tháng 7 2016
(1 - 1/3) × (1 - 1/6) × (1 - 1/10) × (1 - 1/15) × ... × (1/780) × a = 1
2/3 × 5/6 × 9/10 × 14/15 × ... × 779/780 × a = 1
4/6 × 10/12 × 18/20 × 28/30 × ... × 1558/1560 × a = 1
1×4/2×3 × 2×5/3×4 × 3×6/4×5 × 4×7/5×6 × ... × 38×41/39×40 × a = 1
1×2×3×4×...×38/2×3×4×5×...×39 × 4×5×6×7×...×41/3×4×5×6×...×40 × a = 1
1/39 × 41/3 × a = 1
41/297 × a = 1
=> a = 297/41
S
21 tháng 7 2016
1 - 1/3) × (1 - 1/6) × (1 - 1/10) × (1 - 1/15) × ... × (1/780) × a = 1
2/3 × 5/6 × 9/10 × 14/15 × ... × 779/780 × a = 1
4/6 × 10/12 × 18/20 × 28/30 × ... × 1558/1560 × a = 1
1×4/2×3 × 2×5/3×4 × 3×6/4×5 × 4×7/5×6 × ... × 38×41/39×40 × a = 1
1×2×3×4×...×38/2×3×4×5×...×39 × 4×5×6×7×...×41/3×4×5×6×...×40 × a = 1
1/39 × 41/3 × a = 1
41/297 × a = 1
=> a = 297/41
L
3
HT
10 tháng 9 2016
\(a=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)
\(a=\frac{1}{1.3}+\frac{1}{2.3}+\frac{1}{2.5}+\frac{1}{3.5}+...+\frac{1}{5.9}\)
\(a=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}\right)\)
\(a=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(a=2\left(\frac{1}{2}-\frac{1}{10}\right)\)
=> \(a=2.\frac{2}{5}\)
=> \(a=\frac{4}{5}\)
10 tháng 9 2016
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{45}\)
\(\Rightarrow\frac{1}{2}A=\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\right)\cdot\frac{1}{2}\)
\(=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)
\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)
\(\Rightarrow A=\frac{2}{5}:\frac{1}{2}=\frac{4}{5}\)
VB
1
TT
3
11 tháng 8 2016
\(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right).\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{780}\right).a=1\)
=> \(\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{779}{780}.a=1\)
=> \(\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{1558}{1560}.a=1\)
=> \(\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{4.7}{5.6}...\frac{38.41}{39.40}.a=1\)
=> \(\frac{1.2.3.4...38}{2.3.4.5...39}.\frac{4.5.6.7...41}{3.4.5.6...40}.a=1\)
=> \(\frac{1}{39}.\frac{41}{3}.a=1\)
=> \(\frac{41}{117}.a=1\)
=> \(a=1:\frac{41}{117}=\frac{117}{41}\)
XO
2 tháng 7 2019
a) 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/45
= 2 x (1/6 + 1/12+ 1/20 + ... + 1/90)
= 2 x (1/2x3 + 1/3x4 + 1/4x5 + ... + 1/9x10)
= 2 x (1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... +1/9 - 1/10)
= 2 x (1/2 - 1/10)
= 2 x 2/5
= 4/5
2 tháng 7 2019
\(a,\frac{1}{2}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)
\(=2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)
\(=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=2.\frac{2}{5}\)
\(=\frac{4}{5}\)
NT
0
=2×(16+112+120+130+...+1
=2×(12×3+13×4+14×5+...+L2×(2×31+3×41+4×51+...+9×101)
=2×(12−13+13−14+14−15+...+19−1
=45