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Lời giải:
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{899}{900}\)
\(=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}.....\frac{29.31}{30^2}\)
\(=\frac{(1.2.3...29)(3.4.5...31)}{(2.3.4...30)(2.3.4...30)}\)
\(=\frac{1.2.3...29}{2.3.4..30}.\frac{3.4.5...31}{2.3.4...30}\)
\(=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)
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Đặt\(A=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{300}\)
Vì\(\frac{1}{101}>\frac{1}{102}>\frac{1}{103}>...>\frac{1}{300}\)
\(\Rightarrow\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\right)+\left(\frac{1}{201}+\frac{1}{202}+...+\frac{1}{300}\right)\)\(>\left(\frac{1}{200}+\frac{1}{200}+...+\frac{1}{200}\right)+\left(\frac{1}{300}+\frac{1}{300}+...+\frac{1}{300}\right)\)(mỗi cái trong ngoặc là một trăm phân số)
\(\Rightarrow\frac{1}{101}+\frac{1}{102}+...+\frac{1}{300}>\left(\frac{1}{200}\right).100+\left(\frac{1}{300}\right).100\)
\(\Rightarrow A>\frac{1}{2}+\frac{1}{3}\)
\(\Rightarrow A>\frac{5}{6}\)
Mà 5/6>2/3=>A>2/3
\(\Rightarrow\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...+\frac{1}{300}\)
Đặt A = \(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...+\frac{1}{300}\)
Vì \(\frac{1}{101}>\frac{1}{102}>\frac{1}{103}>...>\frac{1}{300}\)
\(\Rightarrow\left(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+....\frac{1}{200}\right)+\left(\frac{1}{201}+\frac{1}{202}+\frac{1}{103}+.....\frac{1}{300}\right)>\left(\frac{1}{200}+\frac{1}{200}+\frac{1}{200}\right)\)
Tự làm tiếp nhé !!!
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Ta có:
A = 3/4 . 8/9 . 15/16 . 24/25 . .... 899/900
= (1.3)/(2.2) . (2.4)/(3.3) . (3.5)/(4.4).....(29.31)/(30.30)
= [(1.2.3...29).(3.4.5...31)]/[(2.3.4...30).(2.3.4...30)]
= [(1.2.3...29)/(2.3.4...30)] . [(3.4.5...31)/(2.3.4...30)]
= (1/30) . (31/2)
= 31/60
Bài này lp 6 mk thi huyện r
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= ( 1 x 3 / 2 x 2 ) . ( 2 x 4 / 3 x 3 ) . ( 3 x 5 / 4 x 4 ) . . . ( 6 x 8 / 7 x 7 ) ( mk viết thế cho rõ nhìn khi lm bỏ ngoặc cx dc )
= 1 x 3 x 2 x 4 x 3 x 4 x ... x 6 x 8 / 2 x 2 x 3 x 3 x 4 x 4 x ... x 7 x 7
= 1 x 8 / 2 x 7
= 8 / 14
= 4/7
Tk nha !!
Ta có :
\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}........\frac{48}{49}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.......\frac{6.8}{7.7}\)
\(=\frac{\left(1.2.3.....6\right).\left(3.4.5.....8\right)}{\left(2.3.4......7\right).\left(2.3.4.....7\right)}\)
\(=\frac{1.2.3.....6}{2.3.4.....7}.\frac{3.4.5......8}{2.3.4......7}\)
\(=\frac{1}{7}.4\)
\(=\frac{4}{7}\)