tính thuận tiện:
3999+2999+2+3999+2999+2
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5999 - 5000 + 4999 - 4000 + 3999 - 3000 + 2999 - 2000 + 1999 - 100
= 999 + 999 + 999 + 999 + 1899
= 999 x 4 + 1899
= 5895
1999-2000+2999-3000+3999-4000+4999-5000+5999-1000
=(1999-2000)+(2999-3000)+(3999-4000)+(4999-5000)+(5999-1000)
=-1+(-1)+(-1)+(-1)+4999
=-1x4+4999
=-4+4999
=4999-4
=4995
1999 - 2000 + 2999 - 3000 + 3999-4000+ 4999-5000+5999-1000
= ( 2000-1999) + ( 3000-2999) + ( 4000-3999) + ( 5999-5000) -1000
= 1 + 1 + 1 + 1 -1000
=4 -1000
= 1000-4
=996
1999 - 2000 + 2999 - 3000 + 3999 - 4000 + 4999 - 5000 + 5999 - 1000
=(1999-2000)+(2999-3000)+(3999-4000)+(4999-5000)+(5999-1000)
=1+(-1)+(-1)+(-1)+4999
=1x4+4999
=4+4999
=4999-4
=4995
tk nha
2-4+6-8+10-12+14-16+18-20+22
=(2+18)-(4+16)+(6+14)-(8+12)-(10+20)+22
=20-20+20-20-20+22
=22-20
=2
Xét mẫu :
\(\frac{2999}{1}+\frac{2998}{2}+.....+\frac{1}{2999}\)
=\(\left(1+\frac{2998}{2}\right)+\left(1+\frac{2997}{3}\right)+....+\left(1+\frac{1}{2999}\right)+1\)
=\(\frac{3000}{2}+\frac{3000}{3}+.....+\frac{3000}{2999}+\frac{3000}{3000}\)
=\(3000\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{3000}\right)\)
Thay vào ta có:
\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{3000}}{3000\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{3000}\right)}\)
=\(\frac{1}{3000}\)
Ta có \(A=\frac{\frac{1}{2}+\frac{1}{3}+....+\frac{1}{3000}}{\frac{2999}{1}+\frac{2998}{2}+...+\frac{1}{2999}}=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{3000}}{\left(1+1+...+1\right)+\frac{2998}{2}+...+\frac{1}{2999}}\)
\(=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{3000}}{\left(1+\frac{2998}{2}\right)+\left(1+\frac{2997}{3}\right)+...+\left(1+\frac{1}{2999}\right)+\frac{3000}{3000}}\)
\(=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{3000}}{\frac{3000}{2}+\frac{3000}{3}+...+\frac{3000}{3000}}\)
= \(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{3000}}{3000\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{3000}\right)}=\frac{1}{3000}\)
Vậy A= \(\frac{1}{3000}\)
\(3999+2999+2+3999+2999+2\\ =\left(3999+2999+2\right)+\left(3999+2999+2\right)\\ =2\cdot\left(3999+2999+2\right)\\ =2\cdot7000\\ =14000\)
\(3999+2999+2+3999+2999+2\)
= \(\left(3999+3999\right)+\left(2999+2999\right)+\left(2+2\right)\)
= \(7998+5998+4\)
= \(13996+4\)
= \(14000\).
Chúc bạn học tốt!