3.3=
Tính nhanh
1.2+2.2+3.3+3.3+....+9.5
giải giúp mk nha
2. Chứng minh rằng : 3.3/20.23+3.3/23.26+....+3.3/77.80<1
\(\dfrac{3.3}{20.23}+\dfrac{3.3}{23.26}+...+\dfrac{3.3}{77.80}\)
\(=3\left(\dfrac{3}{20.23}+\dfrac{3}{23.26}+...+\dfrac{3}{77.80}\right)\)
\(=3\left(\dfrac{1}{20}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{26}+...+\dfrac{1}{77}-\dfrac{1}{80}\right)\)
\(=3\left(\dfrac{1}{20}-\dfrac{1}{80}\right)\)
\(=3.\dfrac{3}{80}=\dfrac{9}{80}< 1\left(đpcm\right)\)
Vậy...
Tính nhanh: a/ 31.64+7.30+146.31 b/ 2^3.3^2.28+2^3.3^5.8
a/
31.64+7.30+146.31=31.(64+146)+7.30
=31.210+7.30=6510+210=6720
b/23.32.28+23.35.8=23.(32.28+35.8)
=23.(9.28+243.8)=8.(252+1944)
=8.2196=17568
Số nguyên x thõa mãn:\(3.3^2.3^3.3^4.3^5...3^x=3^{190}\)
=> 1+2+3+4+5+....+x = 190
x(x+1) = 190.2 = 380
x(x+1) = 19.(19 + 1)
VẬy x = 19
Tìm số nguyên x thỏa mãn:
\(3.3^2.3^3.3^4.....3^x=3^{190}\)
3.32.33.34......3x=3190
=>3(1+2+3+...........+x)=3190
=>1+2+3+.........+x=190
=>\(\frac{x.\left(x+1\right)}{2}\)=180
=>x.(x+1)=190.2
=>x.(x+1)=380
=>x=19
Tìm số nguyên x > 0 thỏa mãn \(3.3^2.3^3.3^4....3^x=3^{190}\)
\(3\cdot3^2\cdot3^3\cdot3^4\cdot....\cdot3^x=3^{190}\)
\(\Leftrightarrow3^{1+2+3+...+x}=3^{190}\)
\(\Leftrightarrow1+2+3+...+x=190\)
\(\Leftrightarrow\dfrac{x\left(x+1\right)}{2}=190\Leftrightarrow x\left(x+1\right)=380\)
\(\Leftrightarrow x^2+x-380=0\)
\(\Leftrightarrow x^2-19x+20x-380=0\)
\(\Leftrightarrow x\left(x-19\right)+20\left(x-19\right)=0\)
\(\Leftrightarrow\left(x-19\right)\left(x+20\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-19=0\\x+20=0\end{matrix}\right.\)\(\Leftrightarrow x=19\left(x>0\right)\)
d) D=1.1! + 2.2! + 3.3! +...+ 6.6!
e) E= 1.1! + 2.2! + 3.3! +...+ n.n!
Mình nhờ các bạn giải cả bài ra giùm mình nhé!!!!
Tính số nguyên x thỏa mãn :
3.3^2.3^3.3^4.............3^x=3^190
Giúp mk bài toán này mi sau mk tick cho!!!!!!!!!!!!!!!!!!!
3.3^2.3^3.............3^x=3^190
3^1+2+3+4+....+x=3^190
nên 1+2+3+.........+x=190
hay (x+1).x :2 =190 nen 190.2= (x+1) . x hay 380 =19.20
vay x=19
3.3=9
366.722=?