Tính B=1+1/2(1+2)+1/3(1+2+3)+....+1/500(1+2+3+...+500)
Những câu hỏi liên quan
tính B= 1+(1/2).(1+2)+(1/3).(1+2+3) +....+(1/500).(1+2+3+4+...+500)
Giúp mềnh hem mình tặng seo
a) Cho A=(1/2-1)(1/3-1).....(1/200-1). hãy so sánh A với -1/199
b) Tính B=1+1/2(1+2)+1/3(1+2+3)...+1/500(1+2+3+...+500)
a, \(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{200}-1\right)\)
\(-A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{200}\right)\)
\(-A=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{199}{200}\)
\(-A=\frac{1}{200}\)
\(A=\frac{-1}{200}>\frac{-1}{199}\)
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tính B=1+1/2x(1+2)+1/3x(1+2+3)+.....+1/500x(1+2+.....+500)
Tính \(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{500}\left(1+2+3+...+500\right)\)
\(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...............+\frac{1}{500}\left(1+2+3+.........+500\right)\)
\(=1+\frac{1}{2}\frac{3.2}{2}+\frac{1}{3}\frac{4.3}{2}+.............+\frac{1}{500}\frac{501.500}{2}\)
\(=\frac{1}{2}\left(2+3+............+501\right)\)
\(=\frac{1}{2}.251000\)
\(=125500\)
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Tính tổng: S = 1-1/2 + 1/3-1/4 + 1/5-1/6 + ..... 1/499-1/500
S = 1-1/2 + 1/3-1/4 + 1/5-1/6 + ..... 1/499-1/500 = (1 + 1/3 + 1/5 + ..+ 1/499) - (1/2 + 1/4 + 1/6 + ...+ 1/500) - (1/2 + 1/4 + 1/6 + ...+ 1/500) + (1/2 + 1/4 + 1/6 + ...+ 1/500) S = (1 + 1/2 + 1/3 + 1/4 + ....+ 1/500) - 2.(1/2 + 1/4 + 1/6 + ...+ 1/500) = (1 + 1/2 + 1/3 + 1/4 + ....+ 1/500)- (1 + 1/2 + 1/3 + ...+1/250) = 1/251 + 1/252 + ...+ 1/500.
Vậy S = 1/251 + 1/252 + ...+ 1/500
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Tính tổng: S = 1-1/2 + 1/3-1/4 + 1/5-1/6 + ..... 1/499-1/500
S = 1-1/2 + 1/3-1/4 + 1/5-1/6 + ..... 1/499-1/500
= (1 + 1/3 + 1/5 + ..+ 1/499) - (1/2 + 1/4 + 1/6 + ...+ 1/500) - (1/2 + 1/4 + 1/6 + ...+ 1/500) + (1/2 + 1/4 + 1/6 + ...+ 1/500)
S = (1 + 1/2 + 1/3 + 1/4 + ....+ 1/500) - 2.(1/2 + 1/4 + 1/6 + ...+ 1/500)
= (1 + 1/2 + 1/3 + 1/4 + ....+ 1/500)- (1 + 1/2 + 1/3 + ...+1/250)
= 1/251 + 1/252 + ...+ 1/500.
Vậy S = 1/251 + 1/252 + ...+ 1/500
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So sánh :A=1-1/2+1/3-1/4+...+1/999-1/1000 và B=500-500/501-501/502-502/503-...-999/1000
1/1*2+1/2*3+1/3*4+............+1/x(x+1)=499/500
Chứng minh rằng:
1) B dfrac{1}{4}+dfrac{1}{5}+dfrac{1}{6}+...+dfrac{1}{19}1
2) Adfrac{1}{5}+dfrac{2}{5^2}+dfrac{3}{5^3}+dfrac{4}{5^4}+...+dfrac{500}{5^{500}}100
3) Cdfrac{1}{2^3}+dfrac{1}{3^3}+dfrac{1}{4^3}+dfrac{1}{5^3}+...+dfrac{1}{500^3}dfrac{1}{4}
4) Ddfrac{4}{3}+dfrac{10}{9}+dfrac{28}{27}+...+dfrac{3^{98}+1}{3^{98}}100
Làm giúp mình sớm nha! Thanks.
Đọc tiếp
Chứng minh rằng:
1) B =\(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{19}>1\)
2) \(A=\dfrac{1}{5}+\dfrac{2}{5^2}+\dfrac{3}{5^3}+\dfrac{4}{5^4}+...+\dfrac{500}{5^{500}}<100\)
3) \(C=\dfrac{1}{2^3}+\dfrac{1}{3^3}+\dfrac{1}{4^3}+\dfrac{1}{5^3}+...+\dfrac{1}{500^3}<\dfrac{1}{4}\)
4) \(D=\dfrac{4}{3}+\dfrac{10}{9}+\dfrac{28}{27}+...+\dfrac{3^{98}+1}{3^{98}}<100\)
Làm giúp mình sớm nha! Thanks.
