1+3+36=?
36/(1*3*5) + 36/(3*5*7) + 36/(5*7*9) + ... + 36/(25*27*29)
CTR:36/1*3*5+36/3*5*7+36/5*7*9+...+36/25*27*29<3
Tính tổng: A=36/(1*3*5)+36/(3*5*7)+36/(5*7*9)+...+36/(45*47*49)
tính nhanh (36 - 1^2).(36 - 2^2).(36 - 3^2)....(36 - 20 ^2 )
(36 - 1²).(36 - 2²).(36 - 3²)...(36 - 20²)
= (36 - 1²).(36 - 2²)...(36 - 6²)...(36 - 20²)
= (36 - 1²).(36 - 2²)...(36 - 36)...(36 - 20²)
= (36 - 1²)(36 - 2²)...0...(36 - 20²)
= 0
a} 3/20+3/30 + 3/42 + ....3/110+3/132
b} 17/36 . 13/15+ 12/15 - 17/36 - 1/36
2 h 30 chiều nay mình phả đi học rồi , làm ơn giúp mình vói mình xin cảm ơn và sẽ k
\(a,\frac{3}{20}+\frac{3}{20}+\frac{3}{42}+...+\frac{3}{132}\)
\(=3\left(\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{11\cdot12}\right)\)
\(=3\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{12}\right)\)
\(=3\left(\frac{1}{4}-\frac{1}{12}\right)\)
\(=3\cdot\frac{1}{6}=\frac{1}{2}\)
a) \(\frac{3}{20}+\frac{3}{30}+\frac{3}{42}+...+\frac{3}{132}\)
= \(3\times\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{132}\right)\)
= \(3\times\left(\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+...+\frac{1}{11\times12}\right)\)
= \(3\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{12}\right)\)
= \(3\times\left(\frac{1}{4}-\frac{1}{12}\right)\)
= \(3\times\frac{1}{6}\)
= \(\frac{1}{2}\)
chứng minh B = 36 / 1 x 3 x 5 + 36 / 3 x 5 x7 + 36 / 5 x 7 x 9 + .... + 36 / 25 x 27 x29 < 3
\(B=\frac{36}{1.3.5}+\frac{36}{3.5.7}+\frac{36}{5.7.9}+...+\frac{36}{25.27.29}\)
\(=9.\left(\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+...+\frac{4}{25.27.29}\right)\)
\(=9.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{25.27}-\frac{1}{27.29}\right)\)
\(=9.\left(\frac{1}{3}-\frac{1}{675}\right)\)
\(=9.\frac{224}{675}\)
\(=\frac{224}{75}\)
THIẾU
\(=\frac{224}{75}< \frac{225}{75}=3\)
Vậy \(B< 3\)
mấy bọn nguuuuuuuuuuuuuuuuuu
2A=\(\frac{2}{1.2.3}\)+\(\frac{2}{2.3.4}\)+...+\(\frac{2}{18.19.20}\)
=1/1.2-1/2.3+1/2.3-1/3.4+...+1/18.19-1/19.20
=1/2-1/19.20
A=1/4-1/19.20.2
vậy A<1/4
E = 36 / 1.7 + 36 / 7.13 + 36 / 13.19 + .... + 36 / 94.100
F = 1 / 10 + 1 / 40 + 1 / 88 + .... + 1 / ( 3a+z) ( 3a+ 5)
G = 1 / 2.3 + 2 / 3.5 + 3 / 5.8 + 4 / 8.12 + 5 / 12.17
E = \(\frac{36}{1\cdot7}+\frac{36}{7\cdot13}+...+\frac{36}{94\cdot100}=\frac{36}{6}\left[\frac{1}{1\cdot7}+\frac{1}{7\cdot13}+...+\frac{1}{94\cdot100}\right]\)
\(=6\left[1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{94}-\frac{1}{100}\right]=6\left[1-\frac{1}{100}\right]\)
\(=6\cdot\frac{99}{100}=\frac{297}{50}\)
F = \(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+...+\frac{1}{\left[3a+2\right]\left[3a+5\right]}\)
\(=\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+...+\frac{1}{\left[3a+2\right]\left[3a+5\right]}\)
\(=\frac{1}{3}\left[\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{3a+2}-\frac{1}{3a+5}\right]\)
\(=\frac{1}{3}\left[\frac{1}{2}-\frac{1}{3a+5}\right]=\frac{1}{6}-\frac{1}{9a+15}\)
G = \(\frac{1}{2\cdot3}+\frac{2}{3\cdot5}+\frac{3}{5\cdot8}+\frac{4}{8\cdot12}+\frac{5}{12\cdot17}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{12}-\frac{1}{17}\)
\(=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)
E=36/1-36/7+36/7-36/13+...+36/94-36/100
=36-36/100=891/25
CMR 36 p 1*3*5+36 p 3*5*7+36 p 5*7*9+....+36 p 25*27*29<3
giúp mình với mình cần gấp 4/9.19/1/3+(-4/9).36/1/3+(-3^2/5):(-0,2) (CHÚ Ý 19/1/3 VÀ 36/1/3 LÀ HỖN SỐ)