\(B=\frac{1}{1.3.5}+\frac{1}{3.5.7}+...+\frac{1}{47.49.51}\)
\(C=\frac{4}{9.11.13}+\frac{4}{11.13.15}+...+\frac{4}{59.61.63}\)
Ai nhanh mik tick nha !!!!!
\(A:\)\(\frac{4}{9.11.13}+\frac{4}{11.13.15}+...+\frac{4}{59.61.63}\)
\(B:\) \(\frac{1}{1.3.5}+\frac{1}{3.5.7}+...+\frac{1}{47.49.51}\)
Đây là bài tính t nha !!!
Ai nhanh mik T>I>C>K
Cho A = \(\frac{1}{1.3.5}\) + \(\frac{1}{3.5.7}\) + ..... + \(\frac{1}{47.49.51}\). Chứng minh A < \(\frac{1}{12}\)
Bài làm:
Ta có: \(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+...+\frac{1}{47.49.51}\)
\(A=\frac{1}{4}\left(\frac{4}{1.3.5}+\frac{4}{3.5.7}+...+\frac{4}{47.49.51}\right)\)
\(A=\frac{1}{4}\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{47.49}-\frac{1}{49.51}\right)\)
\(A=\frac{1}{4}\left(\frac{1}{3}-\frac{1}{49.51}\right)\)
\(A=\frac{1}{12}-\frac{1}{4.49.51}< \frac{1}{12}\)
Vậy \(A< \frac{1}{12}\)
Từ đề bài suy ra\(4A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+...+\frac{4}{47.49.51}\)
\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{47.49}-\frac{1}{49.51}=\frac{1}{3}-\frac{1}{49.51}< \frac{1}{3}\)
\(\Rightarrow A< \frac{1}{12}\left(đpcm\right)\)
\(4A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+...+\frac{4}{47.49.51}\)
\(4A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{47.49}-\frac{1}{49.51}\)
\(4A=\frac{1}{1.3}-\frac{1}{49.51}=\frac{1}{3}-\frac{1}{2499}< \frac{1}{3}\)
=> \(A< \frac{1}{3}:4=\frac{1}{12}\)
VẬY TA CÓ ĐPCM.
NẾU ĐÚNG MONG MỌI NGƯỜI ỦNG HỘ Ạ
\(\frac{4}{1.2.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+\frac{4}{7.9.11}+\frac{4}{9.11.13}\)
tính
=1/1.3-1/3.5+1/3.5-1/5.7+...+1/99.11-1/11.13
=1/1.3-1/11.13
=1/3-1/143
=140/429
Chứng minh rằng :
B=\(\frac{36}{1.3.5}+\frac{36}{3.5.7}+...+\frac{36}{25.27.29}<3\)
C= \(\frac{1}{4^2}+\frac{1}{6^2}+....+\frac{1}{\left(2n\right)^2}<\frac{1}{4}\left(n\in N;n\ge2\right)\)
Giúp mik nhé
\(\begin{equation} x = a_0 + \cfrac{1}{740_1 + \cfrac{1}{897654_2 + \cfrac{1}{672_3 + \cfrac{1}{100_4} } } } \end{equation}\)
tính giá trị của các biểu thức
a) A= \(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{98.99.100}\)
b) B= \(\frac{17}{1.3.5}+\frac{17}{3.5.7}+...+\frac{17}{47.49.51}\)
a) \(A=\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+...+\frac{2}{98\cdot99\cdot100}\)
\(A=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{98\cdot99}-\frac{1}{99\cdot100}\)
\(A=\frac{1}{2}-\frac{1}{99\cdot100}=\frac{1}{2}-\frac{1}{9900}=\frac{4949}{9900}\)
b) \(B=\frac{17}{1\cdot3\cdot5}+\frac{17}{3\cdot5\cdot7}+\frac{17}{5\cdot7\cdot9}+...+\frac{17}{47\cdot49\cdot51}\)
\(B=\frac{17}{4}\left(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+...+\frac{4}{47\cdot49\cdot51}\right)\)
\(B=\frac{17}{4}\left(\frac{1}{1\cdot3}-\frac{1}{3\cdot5}+\frac{1}{3\cdot5}-\frac{1}{5\cdot7}+...+\frac{1}{47\cdot49}-\frac{1}{49\cdot51}\right)\)
\(B=\frac{17}{4}\left(\frac{1}{3}-\frac{1}{2499}\right)=\frac{17}{4}\cdot\frac{832}{2499}=\frac{208}{147}\)
TÌm các số a,b ,c thỏa mãn \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{4}{5}\)
Ai đúng và nhanh mik tick cho nha! :)
Tính nhanh:
\(a)\)\(\frac{4}{1.3.5}\)\(+\frac{4}{3.5.7}\)\(+\frac{4}{5.7.9}\)\(+\frac{4}{7.9.11}\)\(+\frac{4}{9.11.13}\)
\(b)\frac{1991}{1990}\)\(\times\frac{1992}{1991}\)\(\times\frac{1993}{1992}\)\(\times\frac{1994}{1993}\)\(\times\frac{995}{997}\)
Tính ọp từ sáng nay mà bài tập nó hoqq tha cho ><
@32526313:
Giải bài đầy đủ ra đi bạn =))
Nói đ/a ai chả nói được (:
Trả lời:
\(a,\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+\frac{4}{7.9.11}+\frac{4}{9.11.13}\)
\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.11}+\frac{1}{9.11}-\frac{1}{11.13}\)
\(=\frac{1}{1.3}-\frac{1}{11.13}=\frac{1}{3}-\frac{1}{143}=\frac{140}{429}\)
\(b,\frac{1991}{1990}\times\frac{1992}{1991}\times\frac{1993}{1992}\times\frac{1994}{1993}\times\frac{995}{997}\)
\(=\frac{1991\times1992\times1993\times1994\times995}{1990\times1991\times1992\times1993\times997}\)
\(=\frac{1994.995}{1990.997}=\frac{997.2.995}{995.2.997}=1\)
Tính :
A = \(\frac{17}{1.3.5}\) + \(\frac{17}{3.5.7}\) + \(\frac{17}{5.7.9}\) + ... + \(\frac{17}{47.49.51}\)
Ủng hộ 2 tick cho !!!
\(=\frac{1}{4}.\left(\frac{17.4}{1.3.5}+\frac{17.4}{3.5.7}+\frac{17.4}{5.7.9}+...+\frac{17.4}{47.49.51}\right)\)
\(=\frac{17}{4}\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{47.49}-\frac{1}{49.51}\right)\)
\(=\frac{17}{4}\left(\frac{1}{3}-\frac{1}{2499}\right)=\frac{17}{4}.\frac{832}{2499}=\frac{208}{147}\)
Chứng minh rằng A = \(\frac{36}{1.3.5}+\frac{36}{3.5.7}+...+\frac{36}{25.27.29}
\(A=9.\left(\frac{4}{1.3.5}+\frac{4}{3.5.7}+...+\frac{4}{25.27.29}\right)\)
\(A=9.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{25.27}-\frac{1}{27.29}\right)\)
\(A=9.\left(\frac{1}{3}-\frac{1}{783}\right)\)
\(A=9.\frac{260}{87}=\frac{260}{87}