a) \(\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}-\dfrac{3}{4}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{72}\)

\(=\dfrac{5+9+1}{15}-\dfrac{27+8+1}{36}+\dfrac{1}{72}=1-1+\dfrac{1}{72}=\dfrac{1}{72}\)

b) \(=\dfrac{1}{5}-\dfrac{1}{5}-\dfrac{3}{7}+\dfrac{3}{7}+\dfrac{5}{9}-\dfrac{5}{9}-\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{7}{13}-\dfrac{7}{13}-\dfrac{9}{16}\)

\(=\dfrac{9}{16}\)

Câu 1 :

a, 8.( -5 ).( -4 ).2

= [ 8.2 ].[( -5 ).(-4 ]

= 16.20

= 320

b, \(1\frac{3}{7}+\frac{-1}{3}+2\frac{4}{7}\)

\(=\frac{10}{7}+\frac{-1}{3}+\frac{18}{7}\)

\(=\frac{11}{3}\)

c, \(\frac{8}{5}.\frac{2}{3}+\frac{-5.5}{3.5}\)

\(=\frac{8}{3}+\frac{-5}{3}\)

\(=\frac{3}{3}=1\)

d, \(\frac{6}{7}+\frac{5}{8}:5-\frac{3}{16}.\left(-2\right)^2\)

\(=\frac{6}{7}+\frac{1}{8}-\frac{3}{16}.4\)

\(=\frac{55}{56}-\frac{3}{4}\)

\(=\frac{13}{56}\)

Câu 2 :

a, 2x + 10 = 16

    2x = 16 + 10

    2x = 26

    x = 26 : 2

    x = 13

b, \(x-\frac{1}{3}=\frac{5}{4}\)

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

\(x=\frac{19}{12}\)

c, \(2x+3\frac{1}{3}=7\frac{1}{3}\)

\(2x+\frac{10}{3}=\frac{22}{3}\)

\(2x=\frac{22}{3}-\frac{10}{3}\)

\(2x=4\)

\(x=4:2\)

\(x=2\)

d, \(\left(\frac{2}{11}+\frac{1}{3}\right)x=\left(\frac{1}{7}-\frac{1}{8}\right).56\)

\(\frac{17}{33}x=1\)

\(x=1-\frac{17}{33}\)

\(x=\frac{16}{33}\)

\(A=1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+...+\dfrac{1}{16}\left(1+2+3+...+16\right)\\ \Rightarrow A=1+\dfrac{1}{2}\cdot\dfrac{2\cdot3}{2}+\dfrac{1}{3}\cdot\dfrac{3\cdot4}{2}+...+\dfrac{1}{16}\cdot\dfrac{16\cdot17}{2}\\ \Rightarrow A=\dfrac{2}{2}+\dfrac{3}{2}+\dfrac{4}{2}+\dfrac{5}{2}+...+\dfrac{16}{2}+\dfrac{17}{2}\\ \Rightarrow A=\dfrac{1}{2}\left(2+3+4+...+17\right)=76\)

ta có

A = \(1+\frac{1+2}{2}+\frac{1+2+3}{3}+\frac{1+2+3+4}{4}+......+\frac{1+2+3+\text{4 +....+16}}{16}\)

xét tổng S = 1+2+3+4+5+......+n  = \(\frac{\left(n+1\right)n}{2}\) lấy \(\frac{S}{n}=\frac{\frac{\left(n+1\right)n}{2}}{n}=\frac{n+1}{2}\)

ta có

A=\(1+\frac{\frac{2\left(2+1\right)}{2}}{2}+\frac{\frac{3\left(3+1\right)}{2}}{3}+\frac{\frac{4\left(4+1\right)}{2}}{4}+\frac{\frac{5\left(5+1\right)}{2}}{5}+......+\frac{\frac{16\left(16+1\right)}{2}}{16}\)

A = \(1+\frac{1+2}{2}+\frac{1+3}{2}+\frac{1+4}{2}+\frac{1+5}{2}+......+\frac{1+16}{2}\)

A = \(1+\frac{1+2+1+3+1+\text{4+1+5+1+6+.....+1+16}}{2}\)

A = \(1+\frac{151}{2}\)

A = \(\frac{153}{2}\)

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