tính nhanh
a)A=54.34-(152-1)(152+1)
b)C=502-492+482-472+...+22-12
tính nhanh
a)A=54.34-(152-1)(152+1)
b)C=502-492+482-472+...+22-12
(14,78-a)/(2,87+a)=4/1
14,78+2,87=17,65
Tổng số phần bằng nhau là 4+1=5
Mỗi phần có giá trị bằng 17,65/5=3,53
=>2,87+a=3,53
=>a=0,66.
a) A= 54 . 34- (152-1).(152+1)
=(5.3)4-154-1
=154-154-1
=-1
a) A= 54.34 -(152-1).(152+1)
=(5.3)4 - (154-1)
= 154 - 154 +1
= 1
C=-502-492+482-472+......+22-12
\(C=50^2-49^2+48^2-47^2+...+2^2-1^2\)
\(=1+2+3+4+...+49+50\)
\(=51\cdot25=1275\)
a) Tính tổng: A= 12+22+32+...+102
b) Tính theo cách hợp lí tổng B= 52+102+152+...+502
\(A=1^2+2^2+3^2+....+10^2\\ A=1^{ }+\left(1+1\right)\cdot2+3\cdot\left(2+1\right)+.....+10\cdot\left(9+1\right)\\ A=1+2\cdot1+2+3\cdot2+3+....+10\cdot9+10\\ A=\left(1+2+3...+10\right)+\left(1\cdot2+3\cdot2+.....+10\cdot9\right)\)
Gọi 1+2+3+...+10 là P
Số số hạng là: (10 - 1) : 1 +1 = 10 (số)
P = (10+1) . 10 : 2 = 55
P = 55
Gọi \(1\cdot2+2\cdot3+....+9\cdot10\) là C
\(C=1\cdot2+2\cdot3+....+9\cdot10\\ 3\cdot C=1\cdot2\cdot3+2\cdot3\cdot3+....+9\cdot10\cdot3\\ 3\cdot C=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+....+9\cdot10\cdot\left(11-8\right)\\ 3\cdot C=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+.....+9\cdot10\cdot11-8\cdot9\cdot10\\ 3\cdot C=9\cdot10\cdot11\\ 3\cdot C=990\\ C=330\)
\(=>A=P+C\\ =>A=55+330\\ A=385\)
b)
\(B=5^2+10^2+15^2+...+50^2\\ B=5^2+\left(2\cdot5\right)^2+\left(3\cdot5\right)^2+....+\left(5\cdot10\right)^2\\ B=5^2+2^2\cdot5^2+3^2\cdot5^2+...+5^2\cdot10^2\\ B=5^2\cdot\left(1+2^2+3^2+....+10^2\right)\\ B=25\cdot\left(1+2^2+3^2+....+10^2\right)\)
\(\left(1+2^2+3^2+....+10^2\right)=A\)
\(=>B=25\cdot A\\ B=25\cdot385\\ B=9625\)
Tính nhanh:
a) 35 2 – 15 2 ; b) 48 2 - 42 2 + 64 - 52 2
c) 72 2 + 144 . 16 + 16 2 - 12 2 d) 43 2 − 11 2 ( 36 , 5 ) 2 − ( 27 , 5 ) 2
Tính nhanh:
a) 15.64 + 25.100 + 36.15 + 60.100;
b) 47 2 + 48 2 - 25 + 94.48;
c) 9 3 - 9 2 .(-l) - 9.11 + (-l).11.
a) Ta có 15.64 + 25.100 + 36.15 + 60.100
= (15.64 + 36.15) + (25.100 + 60.100)
= 100.(15 + 85) = 10000.
b) Ta có 47 2 + 48 2 - 25 + 94.48
= ( 47 2 +2.47.48+ 48 2 ) - 5 2 = ( 47 + 48 ) 2 - 5 2 =9000.
c) Ta có 93 -92.(-l)-9.11 + (-l).ll
= (93 +92)-(9.11 + 1.11)
= 92(9 +1) -ll.(9 + l) = 700.
Tính nhanh
a) A = 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56
b) B = 1/15 + 1/35 + 1/63 + 1/99 + 1/143
c) C = 1/2 + 1/14 + 1/35 + 1/65 + 1/104 + 1/152
\(B=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\)
\(=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}+\frac{1}{11\cdot13}\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{13}\right)=\frac{5}{39}\)
Tích: 2× 12× 22× ........× 152× 162 =?
Nhanh mình tịck nha
Thực hiện phép tính
a) 9 10 − 15 16 . 5 12 − 11 15 − 7 20
b) 64 + 2 − 3 2 − 7 1 , 69 + 3. 25 16
c) − 2 , 25 + 4 − 2 , 15 2 − 3 7 6 2 . 1 9 16
d) − 1 3 15 + − 2 3 2 : 2 2 3 − − 5 6
e) 15. − 1 5 2 + 1 5 − 2. − 1 2 3 − 1 2
f) − 1 7 . 9 1 2 − 8 , 75 : 2 7 + 0 , 625 : 1 2 3
g) 2 − 1 + 5 2 3 .5 − 6 + 4 − 3 .32 − 2. − 3 2 . 1 9
h) 2 2 − − 5 7 0 + 1 3 4 .3 6
a) 7896-(2345+7896)+(1345-500)
b) 465-38 {456-[-12+103]}
c)-157(-1326+825)-(248+326)
d)90-89+88-87+86-85+.....+2-1
e)-2+7-12+17-22+.....-152+157
b,tui ko bít
c,ko bít àcác phần còn lại làm như thếM = 1002– 992 + 982 – 972 + … + 22 – 12;
N = (202+ 182 + 162 + … + 42 + 22) – (192 + 172 + 152 + … + 32 + 12);
P = (-1)n.(-1)2n+1.(-1)n+1.
a:
Số số hạng trong dãy M là:
(1002-12):10+1=100(số)
=>Sẽ có 50 cặp (1002;992); (982;972);....;(22;12) có hiệu bằng 10
\(M=1002-992+982-972+...+22-12\)
\(=\left(1002-992\right)+\left(982-972\right)+...+\left(22-12\right)\)
\(=10+10+...+10\)
=10*50=500
b: \(N=\left(202+182+...+42+22\right)-\left(192+172+...+32+12\right)\)
\(=\left(202-192\right)+\left(182-172\right)+...+\left(22-12\right)\)
=10+10+...+10
=10*10=100