A=3/7x10+3/10x13+3/13x16+..........+3/97x100. = ?
tính tổng sau bằng cách hợp lý nhất: A= 3/7x10+ 3/10x13+ 3/13x16 +...+ 3/97x100
\(A=\dfrac{3}{7x10}+\dfrac{3}{10x13}+\dfrac{3}{13x16}+...+\dfrac{3}{97x100}\)
\(A=3x\left(\dfrac{1}{7x10}+\dfrac{1}{10x13}+\dfrac{1}{13x16}+...+\dfrac{1}{97x100}\right)\)
\(A=3x\dfrac{1}{3}x\left(\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)
\(A=3x\dfrac{1}{3}x\left(\dfrac{1}{7}-\dfrac{1}{100}\right)\)
\(A=1x\left(\dfrac{100}{700}-\dfrac{7}{700}\right)=\dfrac{93}{700}\)
3 Tính nhanh
3/1x4+3/4x7+3/7x10+3/10x13+3/13x16=?
=1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16
=1-1/16=15/16
Tính nhanh
A=3²/1x4+3² /4x7+3²/7x10+3²/11x12+3²/13x16+. .... +3²/97x100
Giúp mình với nhé
Tính
3 3 3 3 3
--- + ------ + ------ + ------ + ------
1x4 4x7 7x10 10x13 13x16
Ta có : \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.......+\frac{1}{13}-\frac{1}{16}\)
\(=1-\frac{1}{16}\)
\(=\frac{15}{16}\)
= 15/16
Tk mình nha!
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tính nhanh:
a:3/1x4 +3/4x7+3/7x10+3/10x13+3/13x16+3/16x19+3/19x22
b: 2015/2016x1/2017+2015/2016:2017/2016+1/2016
ai nhanh mk tick
trong ngày mai và tối nay
Tính :
A = 1/1x4+1/4x7+1/7x10+1/10x13+1/13x16
1/1.4+1/4.7+1/7.10+1/10.13+1/13.16
=1/3.(3/1.4+3/4.7+3/7.10+3/10.13+3/13.16)
=1/3.(1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)
=1/3.(1/1-1/16)
=1/3.(16/16-1/16)=1/3.15/16=5/16
\(\frac{3}{1x4}\)+\(\frac{3}{4x7}\)+\(\frac{3}{7x10}\)+\(\frac{3}{10x13}\)+..........+\(\frac{3}{97x100}\)
tính nhanh phân số nha mấy bn
mink cần gấp ai nhanh mink tick
3/1x4+3/4x7+...+3/97x100
=1-1/4+1/4-1/7+1/7-...+1/97-1/100
=1-1/100
=99/100
\(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{97.100}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
A=3^2/1x4+3^2/4x7+3^2/7x10+...+3^2/97x100
\(A=3\times\left(\frac{3}{1\times4}+\frac{3}{4\times7}+\frac{3}{7\times10}+...+\frac{3}{97\times100}\right)\)
\(A=3\times\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(A=3\times\left(1-\frac{1}{100}\right)\)
\(A=3\times\frac{99}{100}\)
\(A=\frac{297}{100}\)
\(A=\frac{3^2}{1.4}+\frac{3^2}{4.7}+\frac{3^2}{7.10}+......+\frac{3^2}{97.100}\)
\(A=3.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+....+\frac{3}{97.100}\right)\)
Đặt \(S=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}\)
Ta có: \(S=\frac{3}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+.....+\frac{3}{97.100}\right)\)
\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{97}-\frac{1}{100}\)
\(S=1-\frac{1}{100}=\frac{99}{100}\)
\(\Rightarrow A=3.S=3.\frac{99}{100}=\frac{297}{100}\)
Các bạn giúp mình với : 3/1x4 + 3/4x7 + 3/7x10 + 3/10x13