A. 1+3+5+......+37+39
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\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{37.39}\)
\(=\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{37.39}\right)\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{37}-\frac{1}{39}\right)\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{39}\right)\)
\(=\frac{1}{2}.\frac{4}{13}=\frac{2}{13}\)
\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{37.39}\)
\(A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{37}-\frac{1}{39}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{39}\right)\)
\(A=\frac{1}{2}.\frac{4}{13}\)
\(A=\frac{2}{13}\)
_Chúc bạn học tốt_
a) \(A=2^{100}-2^{99}-2^{98}-...-2^2-2^1\)( Có 2 câu nên mình tính nhanh luôn nhé )
\(\Leftrightarrow A=2^{100}-\left(2^1+2^2+2^3+...+2^{98}+2^{99}\right)\)
\(A=2^{100}-\left(2^{100}-2^1\right)=2^{100}-2^{100}+2=2\)
b) \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{36.37.38}+\frac{1}{37.38.39}\)
\(=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{38-36}{36.37.38}+\frac{39-37}{37.38.39}\)
\(=\left(\frac{3}{1.2.3}-\frac{1}{1.2.3}\right)+\left(\frac{4}{2.3.4}-\frac{2}{2.3.4}\right)+...+\left(\frac{39}{37.38.39}-\frac{37}{37.38.39}\right)\)
\(=\left(\frac{1}{2}-\frac{2}{3}\right)+\left(\frac{2}{3}-\frac{3}{4}\right)+\left(\frac{3}{4}-\frac{4}{5}\right)+...+\left(\frac{1}{37.38}-\frac{1}{38.39}\right)\)
\(=\frac{1}{2}-\frac{2}{3}+\frac{2}{3}-\frac{3}{4}+\frac{3}{4}-\frac{4}{5}+...+\frac{1}{37.38}-\frac{1}{38.39}\)
\(=\frac{1}{2}-\frac{1}{38.39}=\frac{741}{1482}-\frac{1}{1482}=\frac{740}{1482}=\frac{370}{741}\)
\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{37.39}\)
\(2.A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{37.39}\)
\(2.A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{37}-\frac{1}{39}\)
\(2.A=\frac{1}{3}-\frac{1}{39}\)
\(2.A=\frac{13}{39}-\frac{1}{39}=\frac{12}{39}=\frac{4}{13}\)
\(A=\frac{4}{13}:2=\frac{4}{13}.\frac{1}{2}=\frac{2}{13}\)
\(B=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{95.96}\)
\(B=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{95}-\frac{1}{96}\)
\(B=\frac{1}{3}-\frac{1}{96}\)
\(B=\frac{32}{96}-\frac{1}{96}=\frac{31}{96}\)
5014-43-41-39-...-5-3-1
=5014-[43+41+39+...+5+3+1]
=5014-[43+1]*[[43-1]:2+1]:2
=5014-484
=4530
Giải
a) 569 : 567 – 340 : 339 = 52 – 31 = 25 – 3 = 22
b) 155 – [ 2 . ( 30 + 5 – 26 ) . ( 24 : 3 )]
= 155 – [ 2 . 9 . 8 ] = 155 – 144 = 11
c) 37 . 143 + 37 . 57 + 1300
= (37 . 143 + 37.57) + 1300
= 37.(143+ 57) + 1300
= 37. 200 + 1300
= 7400 + 1300
8700.
Số số hạng của dãy đó là:
( 39 - 1) : 2 + 1 = 20 ( số)
Tổng trên là:
( 39 + 1) x 20 : 2 = 400
Khoảng cách : \(2\)
Số các số hạng là : \(\left(39-1\right):2+1=20\left(số\right)\)
Tổng của A là :\(\left(39+1\right)\times20:2=400\)