tÍnh giá trị của biểu thức sau:
Q=1+1/2 (1+2)+1/3 (1+2+3)+.....+1/16(1+2+3+....+16)
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\(A=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16}\left(1+2+...+16\right)\)
\(=1+\frac{1}{2}\cdot\frac{2.3}{2}+\frac{1}{3}\cdot\frac{3.4}{2}+...+\frac{1}{16}\cdot\frac{16.17}{2}\)
\(=1+\frac{3}{2}+\frac{4}{2}+...+\frac{17}{2}\)
\(=\frac{2}{2}+\frac{3}{2}+...+\frac{17}{2}=\frac{1}{2}\left(2+3+...+17\right)=\frac{1}{2}\cdot\frac{16.19}{2}=4.19=76\)
Đặt A = ( 3 + 1 )( 32 + 1 )( 34 + 1 )( 38 + 1 )( 316 + 1 )( 332 + 1 )
=> 2A = 2.( 3 + 1 )( 32 + 1 )( 34 + 1 )( 38 + 1 )( 316 + 1 )( 332 + 1 )
= ( 3 - 1 )( 3 + 1 )( 32 + 1 )( 34 + 1 )( 38 + 1 )( 316 + 1 )( 332 + 1 )
= ( 32 - 1 )( 32 + 1 )( 34 + 1 )( 38 + 1 )( 316 + 1 )( 332 + 1 )
= ( 34 - 1 )( 34 + 1 )( 38 + 1 )( 316 + 1 )( 332 + 1 )
= ( 38 - 1 )( 38 + 1 )( 316 + 1 )( 332 + 1 )
= ( 316 - 1 )( 316 + 1 )( 332 + 1 )
= ( 332 - 1 )( 332 + 1 )
= 364 - 1
2A = 364 - 1 => A = \(\frac{3^{64}-1}{2}\)
Ta có: \(\left(3\dfrac{3}{4}+\dfrac{4}{7}\cdot\dfrac{7}{16}\right):\dfrac{1}{2}\)
\(=\left(\dfrac{15}{4}+\dfrac{1}{4}\right)\cdot2\)
\(=4\cdot2=8\)
Lời giải:
$=(\frac{3}{5}+\frac{2}{5})+(\frac{5}{11}+\frac{16}{11})+(\frac{7}{13}+\frac{19}{13})$
$=\frac{5}{5}+\frac{22}{11}=\frac{26}{13}=1+2+2=5$
a: Ta có: \(x=\sqrt{28-16\sqrt{3}}+2\sqrt{3}\)
\(=4-2\sqrt{3}+2\sqrt{3}\)
=4
Thay x=4 vào B, ta được:
\(B=\dfrac{2-4}{2}=-1\)
Q = 1+ \(\dfrac{1}{2}\) .(1+2)+ \(\dfrac{1}{3}\) . (1 + 2 + 3) +...+ \(\dfrac{1}{16}\) (1+2+3+...+16)
Q = = 1 + \(\dfrac{1}{2}\) .\(\dfrac{2.3}{2}\) + \(\dfrac{1}{3}\) .\(\dfrac{3.4}{2}\) +...+ \(\dfrac{1}{16}\). \(\dfrac{16.17}{2}\)
Q = \(\dfrac{2}{2}+\dfrac{3}{2}+\dfrac{4}{2}+...+\dfrac{17}{2}\)
Q = \(\dfrac{1}{2}\left(3+4+...+17\right)\)
Q = 76