\(3^2\times\left[\left(5^2-3\right)\div11\right]-2^4+2\times10^3\)

\(=9\times\left[\left(25-3\right)\div11\right]-16+2\times1000\)

\(=9\times\left(22\div11\right)-16+2000\)

\(=9\times2-16+2000\)

\(=18-16+2000\)

\(=2+2000\)

\(2002\)

a) Giá trị của biểu thức a là:

a

= 3.10^3 + 2x10^2 + 5.10

= 3.1000 + 2.100 + 5.10

= 3000 + 200 + 50

= 3250

b) Giá trị của biểu thức b là:

b = 35 - 2.1^111 + 3.7.7^2

= 35 - 2.1^111 + 3.7.49

= 35 - 2.1 + 3.7.49

= 35 - 2 + 1029

= 1062

c) Giá trị của biểu thức c là:

c = 5.4^3 + 2.3 + 81.2

= 5.64 + 6 + 162

= 320 + 6 + 162

= 488

488

Ta có: \(A=1\cdot99+2\cdot98+\cdots+99\cdot1\)

\(=2\left(1\cdot99+2\cdot98+\cdots+49\cdot51\right)+50\cdot50\)

\(=2\left\lbrack1\left(100-1\right)+2\left(100-2\right)+\cdots+49\left(100-49\right)\right\rbrack+2500\)

\(=2\cdot\left\lbrack100\left(1+2+\cdots+49\right)-\left(1^2+2^2+\cdots+49^2\right)\right\rbrack+2500\)

\(=2\cdot\left\lbrack100\cdot49\cdot\frac{50}{2}-\frac{49\left(49+1\right)\left(2\cdot49+1\right)}{6}\right\rbrack+2500\)

\(=2\cdot\left\lbrack100\cdot49\cdot25-\frac{49\cdot50\cdot99}{6}\right\rbrack+2500\)

\(=2\cdot\left\lbrack100\cdot49\cdot25-49\cdot25\cdot33\right\rbrack+2500=2\cdot25\cdot49\left(100-33\right)+2500\)

\(=50\cdot49\cdot67+2500=166650\)

Sửa đề: \(B=1\cdot101+2\cdot102+\cdots+9\cdot109\)

\(=1\left(100+1\right)+2\left(100+2\right)+\cdots+9\left(100+9\right)\)

=100(1+2+...+9)+(\(1^2+2^2+\cdots+9^2\) )

\(=100\cdot9\cdot\frac{10}{2}+\frac{9\left(9+1\right)\left(2\cdot9+1\right)}{6}\)

\(=900\cdot5+\frac{9\cdot10\cdot19}{6}=4500+3\cdot5\cdot19=4500+15\cdot19\)

=4500+285

=4785

A+B

=166650+4785

=171435

kb với mik để mik giải tiếp cho nha

\(\dfrac{101}{2}.\dfrac{102}{2}.\dfrac{103}{2}.\dfrac{104}{2}.....\dfrac{200}{2}\\ =\dfrac{101.102.103.104.....200}{2^{100}}\\ =\dfrac{\left(101.102.103.....200\right)\left(1.2.3.....100\right)}{2^{100}.\left(1.2.3.....100\right)}\\ =\dfrac{1.2.3.....200}{\left(2.1\right)\left(2.2\right)\left(2.3\right).....\left(2.100\right)}\\ =\dfrac{\left(1.3.5.....199\right)\left(2.4.6.....200\right)}{4.6.8.....200}\\ =1.3.5.7.....197.199\)

=> Điều phải chứng minh

hay

\(a,2.10^3+6.10^2+0.10+1=2.1000+6.100+0+1=2601\\ b,5.10^4+7.10^3+9.10^2+1.10+5\\ =5.10000+7.1000+9.100+10+5 =57915\)

a) \(...=2000+600+0+1=2601\)

b) \(...=50000+7000+900+10+5=57915\)

\(\frac{101}{2}\times\frac{102}{2}\times\frac{103}{2}\times...\times\frac{200}{2}\)

\(=\frac{1.2.3.....100.101.102.103.....200}{1.2.3.....100.2^{100}}\)

\(=\frac{\left(1.3.5.....199\right).\left(2.4.6.....200\right)}{\left(1.2\right).\left(2.2\right).\left(3.2\right).....\left(100.2\right)}\)

\(=1.3.5.....199\)

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