Các câu hỏi tương tự
\(C=\left(1-\frac{2}{2\cdot3}\right)\cdot\left(1-\frac{2}{3\cdot4}\right)\cdot\left(1-\frac{2}{4\cdot5}\right)\cdot....\cdot\left(1-\frac{2}{99\cdot100}\right)\)
A = \(\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)\cdot.....\cdot\left(1+\frac{1}{2011\cdot2013}\right)\)
Bài 1:
a) \(\frac{1}{1}\cdot2+\frac{1}{2}\cdot3+\frac{1}{3}\cdot4+...+\frac{1}{n}\cdot\left(n+1\right)\)
b) \(\frac{1}{1}\cdot2\cdot3+\frac{1}{2}\cdot3\cdot4+\frac{1}{3}\cdot4\cdot5+...+\frac{1}{a}\cdot\left(a+1\right)\cdot\left(a+2\right)\)
Tính:
B= \(\left(1-\frac{2}{2\cdot3}\right)\) \(\left(1-\frac{2}{3\cdot4}\right)\) \(\left(1-\frac{2}{4\cdot5}\right)...\left(1-\frac{2}{99\cdot100}\right)\)
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, \(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{n^2}< \frac{5}{4}\)
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
Tinh \(B=\left(\frac{1}{2^2}-1\right)\cdot\left(\frac{1}{3^2}-1\right)\cdot\left(\frac{1}{4^2}-1\right)\cdot....\cdot\left(\frac{1}{98^2}-1\right)\cdot\left(\frac{1}{99^2}-1\right)\)
Tính giá trị của biểu thức:a,(32)2-(-23)2-(-52)3b,left|frac{-1}{2}right|^2cdotleft(-32right)-left(-8right)+left|frac{1}{2}right|^3c,2^3+3cdotleft(frac{-5}{86}right)^0cdotleft(frac{1}{2}right)^2cdot4+left[left(-2right)^2:frac{1}{2}right]:8d,left|frac{5}{7}cdotleft(-14right)right|-left(frac{2}{3}right)^2cdotleft(-18right)+6^2cdotfrac{-1}{18}
Đọc tiếp
Tính giá trị của biểu thức:
a,(32)2-(-23)2-(-52)3
b,\(\left|\frac{-1}{2}\right|^2\cdot\left(-32\right)-\left(-8\right)+\left|\frac{1}{2}\right|^3\)
c,\(2^3+3\cdot\left(\frac{-5}{86}\right)^0\cdot\left(\frac{1}{2}\right)^2\cdot4+\left[\left(-2\right)^2:\frac{1}{2}\right]:8\)
d,\(\left|\frac{5}{7}\cdot\left(-14\right)\right|-\left(\frac{2}{3}\right)^2\cdot\left(-18\right)+6^2\cdot\frac{-1}{18}\)
tính S1
\(S_1=\frac{1}{1\cdot2\cdot3\cdot4\cdot5}\)\(+\frac{1}{2\cdot3\cdot4\cdot5\cdot6}+.................+\frac{1}{\left(n-2\right)\left(n-1\right)n\left(n+1\right)\left(2\right)}\)