số các số hạng là:

    (101-1)/1+1=101(số)

tổng các số là:

     (101+1)*101/2=5151

              Đáp số: 5151

A = 10² - ( 5² . 4 - 4³ . 3 ) + 2³

A = 100 - ( 25 . 4 - 64 . 3 ) + 8

A = 100 - ( 100 - 192 ) + 8

A = 100 - ( - 92 ) + 8

A = 192 + 8

A = 200

10^2 - ( 5^2 . 4 - 4^3 . 3 ) + 2^3

= 100 - ( 25 . 4 - 64 . 3 ) + 8

= 100 - ( 100 - 192 ) + 8

= 100 - ( -92 ) + 8

= 192 + 8

= 200

= 251 

\(\dfrac{3}{4}\cdot\dfrac{2}{5}+\dfrac{3}{4}\cdot\dfrac{2}{5}\)

\(=\dfrac{3}{4}\cdot\dfrac{2}{5}\left(1+1\right)\)

\(=\dfrac{6}{20}\cdot2\)

\(=\dfrac{12}{20}=\dfrac{3}{5}\)

3/5 

cái con củ lồn mày

Giúp 

a) \(\dfrac{2}{9}+\dfrac{3}{5}-\dfrac{1}{15}=\dfrac{37}{45}-\dfrac{1}{15}=\dfrac{37}{45}-\dfrac{3}{45}=\dfrac{34}{45}\)

b) \(\dfrac{5}{12}\times\dfrac{4}{5}\div4=\dfrac{1}{3}\div4=\dfrac{1}{12}\)

c) \(\dfrac{8}{9}-\dfrac{4}{15}\div\dfrac{2}{5}=\dfrac{8}{9}-\dfrac{2}{3}=\dfrac{8}{9}-\dfrac{6}{9}=\dfrac{2}{9}\)

A=10^2-(5^2.4-4^3.3)+2^3

A=100-(25.4-64.3)+2^3

A=100-(100-192)+8

A=100-100+192+8

A=0+192+8

A=200

\(\dfrac{1}{\sqrt{3-2\sqrt{2}}}+\dfrac{1}{\sqrt{5-2\sqrt{6}}}\)

\(=\dfrac{1}{\sqrt{\left(\sqrt{2}\right)^2-2\cdot\sqrt{2}\cdot1+1^2}}+\dfrac{1}{\sqrt{\left(\sqrt{3}\right)^2-2\cdot\sqrt{3}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}\)

\(=\dfrac{1}{\sqrt{\left(\sqrt{2}-1\right)^2}}+\dfrac{1}{\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}}\)

\(=\dfrac{1}{\left|\sqrt{2}-1\right|}+\dfrac{1}{\left|\sqrt{3}-\sqrt{2}\right|}\)

\(=\dfrac{1}{\sqrt{2}-1}+\dfrac{1}{\sqrt{3}-\sqrt{2}}\)

\(=\dfrac{\sqrt{2}+1}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}+\dfrac{\sqrt{3}+\sqrt{2}}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}\)

\(=\dfrac{\sqrt{2}+1}{\left(\sqrt{2}\right)^2-1}+\dfrac{\sqrt{3}+\sqrt{2}}{\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2}\)

\(=\sqrt{2}+1+\sqrt{3}+\sqrt{2}\)

\(=2\sqrt{2}+\sqrt{3}+1\)

\(A=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}\)

\(A=\frac{1}{\left(1+2\right).2:2}+\frac{1}{\left(1+3\right).3:2}+\frac{1}{\left(1+4\right).4:2}+\frac{1}{\left(1+5\right).5:2}\)

\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}\)

\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{6}\right)\)

\(A=2.\frac{1}{3}=\frac{2}{3}\)