CMR: 1/1005+1/1006+1/1007+...+1/2009+ 1-1/2+1/3-1/4+...+1/2008+1/2009
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CMR: 1/1005+1/2006+...+1/2009=1-1/2+1/3-1/4+...-1/2008+1/2009
tính: (2011 – 2009) + (2007 - 2005) + … + (7 - 5) + (3 - 1) là:A. 1005 ; B. 1006 ; C.1007 ; D.1008 . ...
1 - 1/2 + 1 /3 - 1/4 + 1/5...........+ 1/2009-1/2010 = 1/1006 + 1007 +....... 1/2010
Ta có :
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2009}-\frac{1}{2010}\)
\(=\left(1+\frac{1}{3}+...+\frac{1}{2009}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2010}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2009}+\frac{1}{2010}\right)-2.\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}...+\frac{1}{2010}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1005}\right)\)
\(=\frac{1}{1006}+\frac{1}{1007}+...+\frac{1}{2010}\)
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Tính giá trị của biểu thức: 12/ 1*3 + 22/ 3*5 + 32/ 5*7 +...... + 10052/ 2009*2011 + 10062/ 2011*2013 + 10072/ 2013*2015
Tính \(\frac{A}{B}\) biết :
A = \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2007}-\frac{1}{2008}\)
B = \(\frac{1}{1005}+\frac{1}{1006}+\frac{1}{1007}+...+\frac{1}{2007}+\frac{1}{2008}\)
Giúp mình nhé
\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2007}-\frac{1}{2008}\)
\(A=\left(1+\frac{1}{3}+...+\frac{1}{2007}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2008}\right)\)
\(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2007}+\frac{1}{2008}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2008}\right)\)
\(A=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2008}-1-\frac{1}{2}-\frac{1}{3}-...-\frac{1}{1004}\)
\(A=\frac{1}{1005}+\frac{1}{1006}+\frac{1}{1007}+...+\frac{1}{2008}\) (1)
\(B=\frac{1}{1005}+\frac{1}{1006}+\frac{1}{1007}+...+\frac{1}{2008}\) (2)
\(\left(1\right)\left(2\right)\Rightarrow\frac{A}{B}=\frac{\frac{1}{1005}+\frac{1}{1006}+\frac{1}{1007}+...+\frac{1}{2008}}{\frac{1}{1005}+\frac{1}{1006}+\frac{1}{1007}+...+\frac{1}{2008}}=1\)
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so sánh 1-1/2+1/3-1/4+....-1/2018 với 1/1005+1/1006+.......+1/2008
cmr:
\(\frac{2009^{2008}-1}{2009^{2009}-1}< \frac{2009^{2007}+1}{2009^{2008}+1}\)
Bài 1 Tính\(\frac{A}{B}\)biết
a)A=\(\frac{1}{1.300}+\frac{1}{2.301}+\frac{1}{3.302}+...+\frac{1}{101.400}\)
B=\(\frac{1}{1.102}+\frac{1}{2.103}+\frac{1}{3.104}+...+\frac{1}{299.400}\)
b)A=1/2+1/3+1/4+...+1/200
B=1/199+2/198+3/197+...+199/1
c)A=1-1/2+1/3-1/4+...+1/2007-1/2008
B=1/1005+1/1006+1/1007+...+1/2007+1/2008
a) 299A = \(1-\frac{1}{400}\) A= \(\frac{399}{400}\) :299
101B = \(1-\frac{1}{400}\) B = \(\frac{399}{400}\):101
\(\frac{A}{B}=\frac{299}{101}\)
Làm tắt ý a, mấy ý kia biết làm nhưng dài lắm
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Tính tổng ( sử dụng máy tính bỏ túi và nêu quy trình bấm phím)
a) S=1/1*2+1/3*4+1/4*5+......+1/99*100
b) S=1^2/1*3+2^2/3*5+3^2/5*7+.........+1005^2/2009*2011+1006^2/2011*2013
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