P=\(\frac{4}{1.3}\) . \(\frac{9}{2.4}\) .....\(\frac{10000}{99.101}\)
=(\(\frac{2.2}{1.3}\)) (\(\frac{3.3}{2.4}\)).... (\(\frac{100.100}{99.101}\))
= \(\frac{\left(2.3....100\right)\left(2.3....100\right)}{\left(1.2....99\right)\left(3.4....101\right)}\)
=\(\frac{100.2}{101}\)
=\(\frac{200}{101}\)
Vậy P = \(\frac{200}{101}\)
Tính
A=\(\left(1-\frac{1}{21}\right)\cdot\left(1-\frac{1}{28}\right)\cdot\left(1-\frac{1}{36}\right)\cdot....\cdot\left(1-\frac{1}{1326}\right)\)
B=\(\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)\cdot....\cdot\left(1+\frac{1}{99\cdot101}\right)\)
Tính tổng A=\(\frac{1}{1\cdot2\cdot3\cdot4}+\frac{1}{2\cdot3\cdot4\cdot5}+\frac{1}{3\cdot4\cdot5\cdot6}+...+\frac{1}{27\cdot28\cdot29\cdot30}\)
\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+.....+\frac{1}{98\cdot99\cdot100}=\frac{1}{k}\cdot\left(\frac{1}{1\cdot2}-\frac{1}{99\cdot100}\right)\)
Số k trong đẳng thức trên có giá trị là ?
Tính nhanh :
\(A=\left(1-\frac{2}{6\cdot7}\right)\left(1-\frac{2}{7\cdot8}\right)\left(1-\frac{2}{8\cdot9}\right)\cdot\cdot\cdot\left(1-\frac{2}{51\cdot52}\right)\)
\(B=\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)\cdot\cdot\cdot\left(1+\frac{1}{99\cdot101}\right)\)
Tính A=\(\frac{1}{2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{98\cdot99}+\frac{1}{99\cdot100}\)
Tính \(A=\frac{1}{1\cdot2\cdot3\cdot4\cdot5}+\frac{1}{2\cdot3\cdot4\cdot5\cdot6}+...+\frac{1}{26\cdot27\cdot28\cdot29\cdot30}\)
a) A = \(\frac{4}{1\cdot2}+\frac{4}{2\cdot3}+\frac{4}{3\cdot4}+.......+\frac{4}{99\cdot100}\)
b) B = \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.......+\frac{1}{45}\)
c) C = \(\frac{6}{1\cdot3}+\frac{6}{3\cdot5}+\frac{6}{5\cdot7}+......+\frac{6}{99\cdot101}\)
e) E = \(\frac{4}{1\cdot3}+\frac{4}{3.5}+\frac{4}{5.7}+......+\frac{4}{205.207}\)
f) F = \(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}\)
- Có 54 số hạng
g) G = \(\frac{1}{5}+\frac{1}{45}+\frac{1}{117}+\frac{1}{221}+...\)
- Tổng này có 20 số hạng
CHÚ Ý : DẤU CHẤM LÀ DẤU NHÂN
Ai giải hộ phép tính này với : \(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{10\cdot11\cdot12}\)
\(A=\frac{1}{2\cdot3}+\frac{1}{6\cdot5}+\frac{1}{10\cdot7}+\frac{1}{14\cdot9}+....+\frac{1}{198\cdot101}\)
