\(B=\left(1-\frac{2}{2.3}\right)\left(1-\frac{2}{3.4}\right)\left(1-\frac{2}{4.5}\right)...\left(1-\frac{2}{99.100}\right)\)
\(B=\frac{4}{2.3}.\frac{10}{3.4}.\frac{18}{4.5}...\frac{9898}{99.100}\)
\(B=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{98.101}{99.100}\)
\(B=\frac{1.2.3...98}{2.3.4...99}.\frac{4.5.6...101}{3.4.5...100}\)
\(B=\frac{1}{99}.\frac{101}{3}=\frac{101}{297}\)
\(C=\left(1-\frac{2}{2\cdot3}\right)\cdot\left(1-\frac{2}{3\cdot4}\right)\cdot\left(1-\frac{2}{4\cdot5}\right)\cdot....\cdot\left(1-\frac{2}{99\cdot100}\right)\)
Tính :
\(\left(1-\frac{2}{2\cdot3}\right)\left(1-\frac{2}{3\cdot4}\right)\left(1-\frac{2}{4\cdot5}\right)\cdot...\cdot\left(1-\frac{2}{99\cdot100}\right)\)
Cần lời giải đầy đủ
Mình sẽ tick
tính S1
\(S_1=\frac{1}{1\cdot2\cdot3\cdot4\cdot5}\)\(+\frac{1}{2\cdot3\cdot4\cdot5\cdot6}+.................+\frac{1}{\left(n-2\right)\left(n-1\right)n\left(n+1\right)\left(2\right)}\)
Bài 1:
a) \(\frac{1}{1}\cdot2+\frac{1}{2}\cdot3+\frac{1}{3}\cdot4+...+\frac{1}{n}\cdot\left(n+1\right)\)
b) \(\frac{1}{1}\cdot2\cdot3+\frac{1}{2}\cdot3\cdot4+\frac{1}{3}\cdot4\cdot5+...+\frac{1}{a}\cdot\left(a+1\right)\cdot\left(a+2\right)\)
Chứng minh:
a, \(\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)\cdot...\cdot\left(1+\frac{1}{n\left(n+2\right)}\right)< 2\)
b, \(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{n^2}< \frac{5}{4}\)
Tính giá trị của biểu thức:
\(A=\frac{1}{2}\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)...\left(1+\frac{1}{2017\cdot2019}\right)\)
A = \(\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)\cdot.....\cdot\left(1+\frac{1}{2011\cdot2013}\right)\)
cho Sn= \(\frac{1}{1\cdot2\cdot3\cdot4}\)+ \(\frac{1}{2\cdot3\cdot4\cdot5}\)+ ... + \(\frac{1}{n\cdot\left(n+1\right)\cdot\left(n+2\right)\cdot\left(n+3\right)}\)
CMR: 18<\(\frac{1}{S_n}\)<=24
\(B=\left(\frac{1}{1\cdot3}\right)\left(\frac{1}{2\cdot4}\right)............\left(\frac{1}{99\cdot101}\right)\)
tính B
đúng tick
