\(S=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{29}-\dfrac{1}{31}=1-\dfrac{1}{31}=\dfrac{30}{31}\)
P=2014/2015=1-1/2015
mà 1/31>1/2015
nên S<P
Bài 12: So sánh S = \(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{27.29}+\dfrac{2}{29.31}\)
P = \(\dfrac{2014}{2015}\)
\(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + \(\dfrac{2}{7.9}\) + ... + \(\dfrac{2}{2020.2022}\)
\(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + ... + \(\dfrac{2}{95.97}\)
\(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...\dfrac{2}{2021.2023}\)
B= \(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) +\(\dfrac{2}{5.7}\) +...+ \(\dfrac{2}{97.99}\) + \(\dfrac{2}{99.101}\)
I.Tìm các giá trị nguyên để biểu thức \(\dfrac{3n+4}{n+2}\) là số nguyên.
II. Cho biểu thức A=\(\dfrac{1}{1.3}\)+\(\dfrac{1}{3.5}\)+\(\dfrac{1}{5.7}\)+...+\(\dfrac{1}{2007.2009}\)
So sánh D với \(\dfrac{2009}{4019}\)
Tính giá trị biểu thức:
B= \(\dfrac{\left(-2\right)^{24}.3^5-4^{12}.9^2}{8^8.3^5}+\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{301.303}\)
Tìm sốtựnhiên x biết: \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+....+\dfrac{1}{x.\left(x+2\right)}=\dfrac{20}{41}\)
a)chứng minh rằng :\(\dfrac{1}{3^2}\)+\(\dfrac{1}{4^2}\)+\(\dfrac{1}{5^2}\)+\(\dfrac{1}{6^2}\)........+\(\dfrac{1}{100^2}< \dfrac{1}{2}\)
b)tính nhanh tổng S với S= \(\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+......+\dfrac{1}{61.63}\)
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