Tính
a, 4\(\times\left(-\dfrac{1}{2}\right)^3-2\times\left(-\dfrac{1}{2}\right)^2+3\times\left(-\dfrac{1}{2}\right)+1\)
b, \(\dfrac{4^6\times9^5+6^9\times120}{-8^4\times3^{12}+6^{11}}\)
c, \(\dfrac{155-\dfrac{10}{7}-\dfrac{5}{11}+\dfrac{5}{23}}{403-\dfrac{26}{7}-\dfrac{13}{11}+\dfrac{12}{23}}+\dfrac{\dfrac{3}{5}+\dfrac{3}{13}-0,9}{\dfrac{7}{91}+0,2-\dfrac{3}{10}}\)
d,\(\dfrac{30\times4^7\times3^{29}-5\times14^5\times2^{12}}{54\times6^{14}\times9^7-12\times8^5\times7^5}\)
tìm x biết \(\dfrac{1}{x}\)-\(\dfrac{1}{9999}\)=\(\dfrac{1}{\begin{matrix}1&\times&3\end{matrix}}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+...+\dfrac{1}{97\times99}\)
Bài 1: Tính
1+\(\dfrac{1}{2}\)×(1+2)+\(\dfrac{1}{3}\)×(1+2+3)+.....+\(\dfrac{1}{16}\)×(1+2+3+....+16)
\(\dfrac{3}{5×7}\) × \(\dfrac{3}{7×9_{ }}\)× .... × \(\dfrac{3}{59×61}\)
Tính:
\(\left(1+\dfrac{7}{9}\right)\times\left(1+\dfrac{7}{20}\right)\times\left(1+\dfrac{7}{33}\right)\times\left(1+\dfrac{7}{48}\right)\times.......\times\left(1+\dfrac{7}{180}\right)\)
Thần đồng nào giỏi toán ! Giúp Mik với nha! Mik xin chân thành cảm ơn!
Chứng tỏ rằng: \(\dfrac{1}{2}< \dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{16}+...+\dfrac{1}{9801}+\dfrac{1}{10000}< \dfrac{37}{50}\)
3, Chứng tỏ :
\(B=\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+...+\dfrac{99}{100!}< 1\)
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 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.