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S = 2(5/1.6 + 5/6.11 +.......+ 5/101.106)
S = 2( 1 - 1/6 + 1/6 - 1/11 +.....+ 1/101 - 1/106)
S = 2( 1 - 1/106)
S = 2 . 105/106
S = 105/53
k mk đi,mk mới bị trừ điểm!
1/2.S=5/(1.6)+5/(6.11)+...+5/(101.106)
1/2.S=1/1-1/6+1/6-1/11+...+1/101-1/106
1/2.S=1/1-1/106
1/2.S=105/106
S=105/53
= 2.(5/1.6+5/6.11+.....+5/56.61)
= 2.(1-1/6+1/6-1/11+.....+1/56-1/61)
= 2.(1-1/61)
= 2.60/61 = 120/61
Tk mk nha
\(\frac{10}{1.6}+\frac{10}{6.11}+...+\frac{10}{56.61}\)
\(=10.\left(\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{56.61}\right)\)
\(=10.\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{56}-\frac{1}{61}\right)\)
\(=2\left(1-\frac{1}{61}\right)\)
\(=2.\frac{60}{61}\)
\(=\frac{120}{61}\)
Đề bài của bạn sai rồi đề đúng phải là 2/1.3 + 5/3.5 + 5/5.7 + ... + 5/101.103
a=5/2.(2/1.3 + 2/3.5 + 2/5.7 + ... + 2/101.103) = 5/2 . ( 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/101 - 1/103)
= 5/2 .(1 - 1/103) = 5/2 . 102/103 = 255/103
câu b tương tự. nhưng đề bài b của bạn cũng sai rồi : 2/1.6 + 2/6.11 + 2/11.16 + ... + 2/101.106
Tính S:
S=5.(\(\dfrac{5}{1.6}\)+\(\dfrac{5}{6.11}\)+...+\(\dfrac{5}{101.106}\))
S=5.(1-\(\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\))
S=5.(1-\(\dfrac{1}{106}\))
S=5.\(\dfrac{105}{106}\)
S=\(\dfrac{525}{106}\)
\(=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)
\(=5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(=5.\left(1-\frac{1}{31}\right)\)
\(=5.\frac{30}{31}\)
\(=\frac{6}{31}\)
\(=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+\frac{5}{26.31}\right)\)
\(=5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}\right)\)
\(=5.\left(1-\frac{1}{31}\right)=\frac{150}{31}\)
2 phần dưới không liên quan gì đến tính chất trên
a) \(A=\frac{5-2}{2.5}+\frac{8-5}{5.8}+...+\frac{20-17}{17.20}\)
\(A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\)
\(A=\frac{1}{2}-\frac{1}{20}=\frac{9}{20}\)
b) \(B=5\left(\frac{6-1}{1.6}+\frac{11-6}{6.11}+...+\frac{106-101}{101.106}\right)\)
\(B=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{101}-\frac{1}{106}\right)\)
\(B=5.\left(1-\frac{1}{106}\right)=\frac{525}{106}\)
bài này dễ nên=> mình lười;mình chỉ ghi kq thôi nha!
=105/106
M=5/28+5/70+5/130+...+5/700.
M=5/4*7+5/7*10+5/10*13+...+5/25*58.
3/5*M=3/4*7+3/7*10+3/10*13+...+3/25*28.
3/5*M=1/4-1/28=3/14.
M=3/14:3/5=5/14.
Vậy M=5/14.
M=5/28+5/70+5/130+.....+5/700
M=1/5x(1/4x7+1/7x10+...+1/25x28)
M=1/5x(1/4-1/7+1/7-1/10+....+1./25-1/28)
M=1/5x(1/4-1/28)
M=1/5x3/14
M=3/70
\(S=2\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{101.106}\right)\)
\(S=2\left(1-\frac{1}{106}\right)\)
\(S=\frac{210}{106}=\frac{105}{53}\)
\(S=2.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{101.106}\right)\)
\(S=2.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-...-\frac{1}{101}+\frac{1}{101}-\frac{1}{106}\right)\)
\(S=2.\left[1+\left(\frac{-1}{6}+\frac{1}{6}\right)+\left(\frac{-1}{11}\frac{1}{11}\right)+...+\left(\frac{-1}{101}+\frac{1}{101}\right)-\frac{1}{106}\right]\)
\(S=2.\left[1+0+0+...+0-\frac{1}{106}\right]\)
\(S=2.\left[1-\frac{1}{106}\right]\)
\(S=2.\frac{105}{106}\)