1] tính nhanh :
3/2 + 7/6 + 13/12 + 21/20 +...+ 111/110 + 133/132
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CM
31 tháng 10 2018
3/2+7/6+13/12+21/20+...+133/132
=1+ 1/2 + 1+ 1/6 + 1+ 1/12 + 1+ 1/20+......+ 1+ 1/132
=(1+ 1 + 1+.....+ 1) + ( 1/2+ 1/6+1/12+ 1/20+....+ 1/132)
= 11+ ( 1/1×2+ 1/2×3+1/3×4+1/4×5+.....+1/11×12)
=11+ ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/11-1/12)
=11+(1-1/12)
= 11+11/12
=143/12
CM
8 tháng 1 2018
3/2+7/6+13/12+21/20+...+133/132 =1+ 1/2 + 1+ 1/6 + 1+ 1/12 + 1+ 1/20+......+ 1+ 1/132 =(1+ 1 + 1+.....+ 1) + ( 1/2+ 1/6+1/12+ 1/20+....+ 1/132) = 11+ ( 1/1×2+ 1/2×3+1/3×4+1/4×5+.....+1/11×12) =11+ ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/11-1/12) =11+(1-1/12) = 11+11/12 =143/12
DD
4
23 tháng 8 2015
A = 1 + 1/110 + 1 + 1/90 + ... + 1 + 1 /2
A = 10 + 1/1.2+ 1 /2.3 + ... + 1/9.10 + 1/10.11
A = 10 + 1/1 - 1/2 + 1 /2 - 1/3 + ... + 1/9 - 1/10 + 1/10 - 1/11
A = 10 + 1/1 - 1/11
A = 10 + 10/11
A = 120/11
HT
23 tháng 8 2015
A = \(\frac{111}{110}+\frac{91}{90}+\frac{73}{72}+...+\frac{13}{12}+\frac{7}{6}+\frac{3}{2}\)
A = \(\left(\frac{1}{2}+1\right)+\left(\frac{1}{6}+1\right)+\left(\frac{1}{12}+1\right)+....+\left(\frac{1}{110}+1\right)\)
A = (1 + 1 + 1 +...+ 1) + \(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)
A = 10 + \(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
A = \(10+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)
A = \(10+\left(1-\frac{1}{11}\right)\)
A = \(10+\frac{10}{11}\)
A = \(\frac{120}{11}\)
NT
0
TG
23 tháng 10 2016
Gọi tổng dãy số hạng trên là A
A = 1 + \(\frac{1}{2}\)+ 1 + \(\frac{1}{6}\)+ 1 + \(\frac{1}{12}\)+ ... + 1 + \(\frac{1}{90}\)+ 1 + \(\frac{1}{110}\)
Mà từ \(\frac{1}{2}\)đén \(\frac{1}{110}\) có 10 số
A = 1 x 10 + \(\frac{1}{2}\)+( \(\frac{1}{2}\)- \(\frac{1}{3}\)) + ( \(\frac{1}{3}\)-\(\frac{1}{4}\)) + (\(\frac{1}{4}\)-\(\frac{1}{5}\)) + ... + \(\frac{1}{11}\)
A = 10 + \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{11}\)= \(\frac{112}{11}\)
VD
14
31 tháng 1 2016
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+..........+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{11.12}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...........+\frac{1}{11}-\frac{1}{12}\)
\(=1-\frac{1}{12}\)
\(=\frac{11}{12}\)
\(=(1+\frac{1}{2})+(1+\frac{1}{6}) + ..+ (1+\frac{1}{132})\)
\(=(1+..+1) + (\frac{1}{2}+\frac{1}{6} + ..+ \frac{1}{132}) \)
\(=66+ (\frac{1}{1.3}+\frac{1}{2.3}+...+ \frac{1}{11.12})\)
\(=66+ (1-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-....+\frac{1}{11}-\frac{1}{12})\)
\(=66+(\frac{1}{2}-\frac{1}{12})= 66+\frac{5}{12}=\frac{797}{12}\)
3/2 + 7/6 + 13/12 + 21/20 +...+ 111/110 + 133/132
=(1+1/2)+(1+1/6)+(1+1/12)+(1+1/20)+...+(1+1/110)+(1+1/132)
=(1+1+...+1)+(1/2+1/6+1/12+...+1/110+1/132)
=(có 11 số 1) 1*11+(1/1*2+1/2*3+1/3*4+1/4*5+...+1/10*11+1/11*12) => 1/1*2=2-1/1*2=2/1*2-1/1*2 1/2*3=3-2/2*3=3/2*3-2/2*3.....
=11+(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/10-1/11+1/11-1/12)
=11+(1-1/12)
=11+11/12
=143/12
*:là dấu nhân