Cho B=\(\dfrac{1}{4^2}+\dfrac{1}{6^2}+\dfrac{1}{8^2}+...+\dfrac{1}{2006^2}\). Chứng minh : B<\(\dfrac{334}{2007}\)
Cho \(A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+................+\dfrac{1}{9^2}\)
Chứng minh \(\dfrac{2}{5}< A< \dfrac{8}{9}\)
Help me!!!!!!!!!!! tôi đang cần gấp!!!
Chứng tỏ rằng: B=\(\dfrac{1}{2^2}+\dfrac{1}{3^2} +\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+\dfrac{1}{8^2}\)<1
Cho \(M=\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+...................+\dfrac{1}{1+2+3+...........+59}\)
Chứng minh \(M< \dfrac{2}{3}\)
Help me!!!!!!!!!!!!!!
Bài 1: Cho b \(\in\) N, b > 1
Chứng minh: \(\dfrac{1}{b}-\dfrac{1}{b+1}< \dfrac{1}{b^2}< \dfrac{1}{b-1}-\dfrac{1}{b}\)
Bài 2: Cho S = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+.....+\dfrac{1}{9^2}\)
Chứng minh: \(\dfrac{2}{5}< S< \dfrac{8}{9}\)
-Giúp tớ với, bí quá :<
b) Cho S = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{9^2}\). Chứng minh rằng \(\dfrac{2}{5}< S< \dfrac{8}{9}\)
Tính tổng sau
B=\(\dfrac{5}{2\cdot1}+\dfrac{4}{1\cdot11}+\dfrac{3}{11\cdot2}+\dfrac{1}{2\cdot15}+\dfrac{13}{15\cdot4}\)
Chứng tỏ rằng
D=\(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}< 1\)
HELP ME
a) Tìm số nguyên a sao cho A=\(\dfrac{a^3+3a^2+2a-3}{a+1}\) có giá trị nguyên
b) Cho B=\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+......+\dfrac{1}{9^2}\). Chứng minh rằng: \(\dfrac{8}{9}>B>\dfrac{2}{5}\)
Cho \(A=\dfrac{2}{3^2}+\dfrac{2}{5^2}+\dfrac{2}{7^2}+.............+\dfrac{2}{2007^2}\)
Chứng minh \(A< \dfrac{1003}{2008}\)
Help me!!!!!!!!!!