tinh B = 3+3/(1+2)+3/(1+2+3)+...+3/(1+2+3+...+100)
Những câu hỏi liên quan
tinh S= 1+1/2(1+2)+1/3(1+2+3)+...+1/100(1+2+3+...+100)
cho bieu thuc a=-1/3+1/3^2-1/3^3+1/3^4-1/3^5+...+1/3^100 tinh gia tri cua bieu thuc b=4/a/+1/3^100
Tinh
A=1+1/2(1+2)+1/3(1+2+3)+...+1/100(1+2+3+...+100)
A = 1 + \(\frac{1}{2}\left(1+2\right)\)+ \(\frac{1}{3}\left(1+2+3\right)\)+ .... + \(\frac{1}{100}\left(1+2+3+...+100\right)\)
A = \(1+\frac{1}{2}\cdot\frac{2.3}{2}+\frac{1}{3}\cdot\frac{3.4}{2}+...+\frac{1}{100}\cdot\frac{100.101}{2}\)
A = \(\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{101}{2}\)
A = \(\frac{2+3+4+...+101}{2}\)
A = \(\frac{\left(101+2\right).100}{2}\div2\)
A = \(5150\div2=2575\)
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Tinh a) (100-12)(100-22)(100-32)...(100-192)
b) (125-13)(125-33)(125-33).....(125-493)
Tinh G=1/3+2/3^2+3/3^3+...+100/3^100
yêu cầu bạn ơi?
\(G=\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}\)
\(3G=1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{100}{3^{99}}\)
\(3G-G=1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{100}{3^{99}}\)\(-\frac{1}{3}-\frac{2}{3^2}-\frac{3}{3^3}-...-\frac{100}{3^{100}}\)
\(2G=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}-\frac{100}{3^{100}}\)
Đặt \(M=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)
\(3M=3+1+\frac{1}{3}+...+\frac{1}{3^{98}}\)
\(3M-M=3+1+\frac{1}{3}+...+\frac{1}{3^{98}}\)\(-1-\frac{1}{3}-\frac{1}{3^2}-...-\frac{1}{3^{99}}\)
\(2M=3-\frac{1}{3^{99}}\Leftrightarrow M=\frac{3}{2}-\frac{1}{3^{99}.2}\)
\(\Rightarrow2G=\frac{3}{2}-\frac{1}{3^{99}.2}-\frac{100}{3^{100}}\)
\(\Rightarrow G=\frac{3}{4}-\frac{1}{3^{99}.2^2}-\frac{100}{3^{100}.2}\)
Tinh:
A= (10^3-1}^1.(10^3-2)^2.(10^3-3)^3.........(10^3-100)^100
tinh nhanh
a) A= 33(1-2/3)(1-2/5)...(1-2/99)
b) B=101+100+99+98+...+3+2+1/101-100+99-98+...+3-2+1
c) C=423134x846267-423133/423133x846267+423134
Bạn giỏi bạn làm đi đã ngu zồi thích tỏ ra minh ngu hơn. Bạn sợ bạn nếu ko nói câu đấy người ta tưởng bạn khôn chắc
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Tinh
B=1/2+2/2^2+3/2^3+4/2^4+.....+99/2^99+100/2^100
\(B=\dfrac{1}{2}+\dfrac{2}{2^2}+\dfrac{3}{2^3}+.......+\dfrac{99}{2^{99}}+\dfrac{100}{2^{100}}\)
\(\Leftrightarrow2B=1+\dfrac{1}{2^2}+\dfrac{2}{2^3}+\dfrac{3}{2^4}+........+\dfrac{98}{2^{99}}+\dfrac{99}{2^{100}}\)
\(\Leftrightarrow2B-B=\left(1+\dfrac{1}{2^2}+\dfrac{2}{2^3}+........+\dfrac{99}{2^{100}}\right)-\left(\dfrac{1}{2}+\dfrac{2}{2^2}+......+\dfrac{100}{2^{100}}\right)\)
\(\Leftrightarrow B=\dfrac{1}{2}+\dfrac{1}{2^2}+..........+\dfrac{1}{2^{100}}-\dfrac{100}{2^{100}}\)
Đặt :
\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+.....+\dfrac{1}{2^{100}}\)
\(\Leftrightarrow2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+........+\dfrac{1}{2^{99}}\)
\(\Leftrightarrow2A-A=\left(1+\dfrac{1}{2}+......+\dfrac{1}{2^{99}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+.....+\dfrac{1}{2^{100}}\right)\)
\(\Leftrightarrow A=1-\dfrac{1}{2^{100}}\)
\(\Leftrightarrow B=1-\dfrac{1}{2^{100}}-\dfrac{100}{2^{100}}\)
\(\Leftrightarrow B=\dfrac{2^{100}-101}{2^{100}}\)
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tinh A=1+ 1/2 +1/(2*3) +1/(3*4)+...+1/(99*100)+100