A = \(\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dfrac{1}{5^2}+...+\dfrac{1}{100^2}\)
A < \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{99.100}\)
A < \(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
A < \(\dfrac{1}{2}-\dfrac{1}{100}\)
⇒ A < \(\dfrac{1}{2}\)
Chứng minh:
\(\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}và< \dfrac{1}{2}\)
Cho A = \(\dfrac{\left(3\dfrac{2}{15}+\dfrac{1}{5}\right):2\dfrac{1}{2}}{\left(5\dfrac{3}{7}-2\dfrac{1}{4}\right):4\dfrac{43}{56}}\) ; B = \(\dfrac{1,2:\left(1\dfrac{1}{5}.1\dfrac{1}{4}\right)}{0,32+\dfrac{2}{25}}\)
Chứng minh rằng A= B
1. Chứng minh:
\(\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}< \dfrac{3}{16}\)
2. Cho:
\(M=\dfrac{1}{15}+\dfrac{1}{105}+\dfrac{1}{315}+...+\dfrac{1}{1977}\). So sánh M với 12.
So sánh :
a) Chứng minh rằng : M = \(\dfrac{1}{2!}+\dfrac{1}{3!}+\dfrac{1}{4!}+.......+\dfrac{1}{100!} \)
Chứng minh rằng : M <1 .
b) Chứng minh rằng : N = \(\dfrac{9}{10!}+\dfrac{9}{11!}+\dfrac{9}{12!}+........+\dfrac{9}{1000!}\)
Chứng minh rằng : N < \(\dfrac{1}{9!}\)
Chứng minh rằng
A= \(\dfrac{1}{2}\). \(\dfrac{3}{4}\).\(\dfrac{5}{6}\)..........\(\dfrac{99}{100}\)< \(\dfrac{1}{10}\)
B= 1+ \(\dfrac{1}{2}\)+\(\dfrac{1}{3}\)+.......+ \(\dfrac{1}{64}\)>4
Chứng tỏ rằng \(C=\dfrac{1}{2}\times\dfrac{3}{4}\times\dfrac{5}{6}\times...\times\dfrac{9999}{10000}< \dfrac{1}{100}\)
Cho S=\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{2015^2}\). Chứng tỏ rằng \(\dfrac{1007}{2016}< S< \dfrac{2014}{2015}\)
Chứng minh rằng :
a) \(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{199}-\dfrac{1}{200}=\dfrac{1}{101}\)+ \(\dfrac{1}{102}+...+\dfrac{1}{200}\)
cho M=\(\dfrac{1}{2}\cdot\dfrac{3}{4}\cdot\dfrac{5}{6}\cdot...\cdot\dfrac{99}{100}\)
N=\(\dfrac{2}{3}\cdot\dfrac{4}{5}\cdot\dfrac{6}{7}\cdot...\cdot\dfrac{100}{101}\)
chứng minh rằng: M<\(\dfrac{1}{10}\)
Em cần gấp câu trả lời cho bài toán này, mong đc mn giúp đỡ (nếu được xin trả lời trước 12h ngày 10/5 giúp em ạ). Cảm ơn mn.