biết \(1^2=2^2+3^2+...10^2=385\) Hãy tính:
A= \(2^2+4^2+6^2+..+20^2\)và B = \(1^2+3^2+6^2+9^2+...+30^2\)
a, Cho biết: \(1^2+2^2+3^2+...+10^2=385\)
Tính A= \(3^2+6^2+9^2+...+30^2\)
b, Cho biết: \(1^3+2^3+3^3+...+10^3=3025\)
Tính B= \(2^3+4^3+6^3+...+20^3\)
a: A=3^2(1^2+2^2+...+10^2)
=9*385
=3465
b: B=2^3(1^3+2^3+...+10^3)
=8*3025
=24200
Cho S=1^2+2^2+3^2+...+10^2=385
Tính: A=2^2+4^2+6^2+...+20^2
B=3^2+6^2+9^2+...+30^2
A = \(2^2.\left(1^2+2^2+3^2+...+10^2\right)=4.385=1540\)
B=\(3^2.\left(1^2+2^2+3^2+...+10^2\right)=385.9=3465\)
Cho biết 1^2+2^2+3^2+...+10^2=385, tính nhanh:
S=2^2+4^2+6^2+...+20^2. ;
P=3^2+6^2+9^2+...+30^2
\(S=2^2+4^2+....+20^2=?\)
\(=\left(2.1\right)^2+\left(2.2\right)^2+\left(2.3\right)^2+....+\left(2.10\right)^2\)
\(=2^2.1^2+2^2.2^2+2^2.2^3+...+2^2.10^2\)
\(=2^2.\left(1^2+2^2+3^2+...+10^2\right)\)
\(=2^2.385\)
\(=4.385\)
\(=1540\)
S=22+42+...+202
=> 1/2 .S=12+22+...+102
=> 1/2 .S=385
=> S = 385 . 2
=> S = 770
P=(1.3)2+...+(10.3)
=32(12+...+102)
=9.385 = 3465
Tính Nhanh
a) B=1/2003.2002-1/2002.2001-.....-1/3.2-1/2.1
b) Cho biết 1^2+2^2+3^2+......+10^2=385
Tính Nhanh S=2^2+4^2+6^2+......+20^2, P=3^2+6^2+9^2+...+30^2
b. S=(2+4+6+...+19+20)^2
P=(3+6+9+...+30)^2
Cho biết 1^2 + 2^3 + 3^2+....+9^2+10^2 =385. Không dùng máy tính cầm tay em hãy tính: S=10^2+20^3+30^2+...+90^2+100^2
Lời giải:
$S=10^2+(10.2)^2+(10.3)^2+...+(10.9)^2+(10.10)^2$
$=10^2(1^2+2^2+3^2+...+9^2+10^2)$
$=100.385=38500$
Tính nhanh P=3^2+6^2+9^2+...+30^2 biết 1^2+2^2+3^2+...+10^2=385
\(P=3^2+6^2+9^2+...+30^2\)
\(=\left(1.3\right)^2+\left(2.3\right)^2+\left(3.3\right)^2+...+\left(10.3\right)^2\)
\(=\left(1^2+2^2+3^2+...+10^2\right).3^2\)
\(=385.9\)
\(=3465\)
Tính:
a) -5/7(14/5 - 7/10) : |-2/3| - 3/4(8/9 + 16/3) + 10/3(1/3 + 1/5)
b) 17/-26(1/6 - 5/3) : 17/13 - 20/3(2/5 - 1/4) + 2/3(6/5 - 9/2)
c) -8/9(9/8 - 3/2) + 5/4 : (5/2 - 15/4) - 3/4(10/9 - 8/3) : (-1/3)
d) 21/10 : (12/5 - 9/10) . (-4/7) - 3/2(1/6 - 7/12) + 1/5(3/2 - 1/4)
a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
Biết 1^2+2^2+3^2+..+9^2+10^2=385
Tính 2^2+4^2+6^2+...+18^2+20^2 bằng bao nhiêu
Ta có : 12+22+32+...+92+102=385
22+42+62+...+202=22.12+22.22+22.32+....+22.92+22.102
=22.(11+22+32+....+92+102)
=4.385
=1540
S = 22 + 42 + 62 + ... + 202
= (2.1)2 + (2.2)2 + (2.3)2 ... (2.10)2
= 22.12 + 22.22 + 22.32 + ... + 22.102
= 22 (12 + 22 + ... + 102 )
= 4 . 385 = 1540
Cho biết $1^2+2^2+3^2+\ldots+10^2=385$
Tính $A=3^2+6^2+9^2+\ldots+30^2$.
A = 3² + 6² + 9² + ... + 30²
= (3.1)² + (3.2)² + (3.3)² + ... + (3.10)²
= 3².(1² + 2² + 3² + ... + 10²)
= 9.385
= 3465