Tính tổng: 1/(2x4x6) + 1/(4x6x8) + 1/(6x8x10) +...+ 1/(96x98x100)
Những câu hỏi liên quan
Tính nhanh
1/2x4x6 +1/4x6x8 + 1/6x8x10 + 1/8x10x12 + ...+ 1/96x98x100
Đặt biểu thức là A
\(4xA=\frac{4}{2x4x6}+\frac{4}{4x6x8}+\frac{4}{6x8x10}+\frac{4}{8x10x12}+...+\frac{4}{94x96x98}+\frac{4}{96x98x100}\)
\(4xA=\frac{6-2}{2x4x6}+\frac{8-4}{4x6x8}+\frac{10-6}{6x8x10}+\frac{12-8}{8x10x12}+...+\frac{98-94}{94x96x98}+\frac{100-96}{96x98x100}\)
\(4xA=\frac{1}{2x4}-\frac{1}{4x6}+\frac{1}{4x6}-\frac{1}{6x8}+\frac{1}{6x8}-\frac{1}{8x10}+...+\frac{1}{94x96}-\frac{1}{96x98}+\frac{1}{96x98}-\frac{1}{98x100}\)
\(4xA=\frac{1}{2x4}-\frac{1}{98x100}=\frac{49x50-1}{98x100}\Rightarrow A=\frac{49x50-1}{4x98x100}\)
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Tính tổng
cho P=2x4x6+4x6x8+6x8x10+...+94x96x98+96x98x100
Ta có G = 2 . 4 + 4 . 6 + 6 . 8 + ... + 98 . 100
6 . G = 2 . 4 . 6 + 4 . 6 . 6 + 6 . 8 . 6 + .... + 98 . 100 . 6
6 . G = 2 . 4 . 6 + 4 . 6 . ( 8 - 2 ) + 6 . 8 . ( 10 - 4 ) + .... + 98 . 100 . ( 102 - 96 )
6 . G = 2 . 4 . 6 + 4 . 6 . 8 - 2 . 4 . 6 + 6 . 8 . 10 - 4 . 6 . 8 + ... + 98 .100 . 102 - 96 . 98 . 100
6 . G = 98 . 100 . 102
G = 98 . 100 . 102 : 6
G = 999 600 : 6
G = 166 600
Ta có G = 2 . 4 + 4 . 6 + 6 . 8 + ... + 98 . 100
6 . G = 2 . 4 . 6 + 4 . 6 . 6 + 6 . 8 . 6 + .... + 98 . 100 . 6
6 . G = 2 . 4 . 6 + 4 . 6 . ( 8 - 2 ) + 6 . 8 . ( 10 - 4 ) + .... + 98 . 100 . ( 102 - 96 )
6 . G = 2 . 4 . 6 + 4 . 6 . 8 - 2 . 4 . 6 + 6 . 8 . 10 - 4 . 6 . 8 + ... + 98 .100 . 102 - 96 . 98 . 100
6 . G = 98 . 100 . 102
G = 98 . 100 . 102 : 6
G = 999 600 : 6
G = 166 600
Đề bài như sau:
1/2x4x6+1/4x6x8+1/6x8x10+1/8x10x12+1/10x12x14+...+1/96x98x100
Giups mình nhé các bạn,mình đang cần cực gấp(khoảng 10 p nữa phải nộp rùi T_T)
Xin các bạn giúp mình.
Cảm ơn các bạn rất nhiều.
1/2x4x6+1/4x6x8+1/6x8x10+......+1/50x52x54
\(\frac{1}{2.4.6}+\frac{1}{4.6.8}+\frac{1}{6.8.10}+..+\frac{1}{50.52.54}\)
\(=\frac{1}{4}.\left(\frac{1}{2.4}-\frac{1}{4.6}+\frac{1}{4.6}-\frac{1}{6.8}+....+\frac{1}{50.52}-\frac{1}{52.54}\right)\)
\(=\frac{1}{4}.\left(\frac{1}{2.4}-\frac{1}{52.54}\right)\)
\(=\frac{1}{4}.\frac{175}{1404}=\frac{175}{5616}\)
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Tính tổng:
A=\(\frac{1}{2x4x6}\)+\(\frac{1}{4x6x8}\)+\(\frac{1}{6x8x10}\)+...+\(\frac{1}{22x24x26}\)
\(A=\frac{1}{3}.\left(\frac{3}{2.4.6}+\frac{3}{4.6.8}+...+\frac{3}{22.24.26}\right)\)
\(A=\frac{1}{3}.\left(\frac{1}{2.4}-\frac{1}{4.6}+\frac{1}{4.6}-\frac{1}{6.8}+...+\frac{1}{22.24}-\frac{1}{24.26}\right)\)
\(A=\frac{1}{3}.\left(\frac{1}{2.4}-\frac{1}{24.26}\right)\)
\(A=\frac{1}{3}.\frac{77}{624}\)
\(A=\frac{77}{1872}\)
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1/2x4x6+1/4x6x8+1/6x8x10+........+1/50x52x54
giai bai tinh nhanh nay ra cho minh nhe
1.1/2x4x6+1/4x6x8+1/6x8x10+....+1/96x98x180
2.(1-3/4) x (1-3/7) x (1-3/10) x...x(1x3/97)x(1-3/100)
Ae giúp tôi, mai nộp r
Giúp mình giải câu hỏi này với:
1x2x3+2x3x4+3x4x5+...+100x101x102/2x4x6+4x6x8+6x8x10+...+200x202x204
\(\frac{5}{2x4x6}+\frac{5}{4x6x8}+\frac{5}{6x8x10}+...+\frac{5}{16x18x20}\)
\(A=\frac{5}{4}.\left(\frac{4}{2.4.6}+\frac{4}{4.6.8}+\frac{4}{6.8.10}+....+\frac{4}{16.18.20}\right)\)
\(=\frac{5}{4}.\left(\frac{1}{2.4}-\frac{1}{4.6}+\frac{1}{4.6}-\frac{1}{6.8}+\frac{1}{6.8}-\frac{1}{8.10}+....+\frac{1}{16.18}-\frac{1}{18.20}\right)\)
\(=\frac{5}{4}.\left(\frac{1}{2.4}-\frac{1}{18.20}\right)=\frac{5}{4}.\frac{11}{90}=\frac{11}{72}\)
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