Tính nhanh:
\(\frac{\left(1+2+4+8+...+512\right)x\left(101x102-101x101-50-51\right)}{2+4+8+16+...+1024+2048}\)
(̣̣1+2+4+8+...+512) x (101x102-101x101-50-51)
Ai làm nhanh và đúng mình sẽ tick cho
( 1 + 2 + 4 + 8+ ... + 512 ) x ( 101 x 102 - 101 x 101 - 50 - 51 )
= ( 1 + 2 + 4 + 8+ ... + 512 ) x ( 101 x 102 - 101 x 101 - 101 )
= ( 1 + 2 + 4 + 8+ ... + 512 ) x ( 101 - 101 )
= ( 1 + 2 + 4 + 8+ ... + 512 ) x 0
= 0
1. Tính hợp lý :
A = \(\frac{\left(1+2+3+...+100\right)x\left(101x102-101x101-50-51\right)}{2+4+8+16...+2048}\)
B = \(\frac{101+100+99+...+3+2+1}{101-100+99-98+...+3-2+1}\)
2. Tìm số tự nhiên x, biết :
a, 697 : \(\frac{15x+364}{x}\)=17
b, 92.4 - 27 = \(\frac{x+350}{x}\)+315
c, 720 : [ 41 - ( 2x -5)] = 40
d, (x+1) + (x+2) +...+ (x+100) = 5750
Câu 1:
\(A=\frac{\left(1+2+3+...+100\right)x\left(101x102-101x101-51-50\right)}{2+4+6+8+...+2048}\)
\(A=\frac{\left(1+2+3+...+100\right)x\left(101x\left(102-101\right)-\left(50+51\right)\right)}{2+4+6+8+...+2048}\)
\(A=\frac{\left(1+2+3+...+100\right)x\left(101-101\right)}{2+4+6+8+...+2048}\)
\(A=\frac{\left(1+2+3+...+100\right)x0}{2+4+6+8+...+2048}\)
\(A=0\)
Ta có:Số số hạng từ 2 đến 101 là:
(101-2):1+1=100(số hạng)
Do đó từ 2 đến 101 có số cặp là:
100:2=50(cặp)
\(B=\frac{101+100+99+...+3+2+1}{101-100+99-98+3-2+1}\)
\(B=\frac{5151}{51}\)
\(B=101\)
Câu 2:
a)697:\(\frac{15x+364}{x}\)=17
\(\frac{15x+364}{x}\)=697:17
\(\frac{15x+364}{x}\)=41
15x+364=41x
41x-15x=364
26x=364
x=14
Vậy x=14
b)92.4-27=\(\frac{x+350}{x}+315\)
\(\frac{x+350}{x}+315\)=341
\(\frac{x+350}{x}\)=26
x+350=26
x=26-350
x=-324
Vậy x=-324
c, 720 : [ 41 - ( 2x -5)] = 40
[ 41 - ( 2x -5)] =720:40
[ 41 - ( 2x -5)] =18
2x-5=41-18
2x-5=23
2x=28
x=14
Vậy x=14
d, Số số hạng từ 1 đến 100 là:
(100-1):1+1=100(số hạng)
Tổng dãy số là:
(100+1)x100:2=5050
Mà cứ 1 số hạng lại có 1x suy ra có 100x
Ta có:(x+1) + (x+2) +...+ (x+100) = 5750
(x+x+...+x)+(1+2+...+100)=5750
100x+5050=5750
100x=700
x=7
Vậy x=7
tính nhanh ;
1234.5678.(630 -315) :1996
319.45+ 55.319 /1995.1996 -1991.1995
1988.1996+1997.11+1985 /1997.1996-1995.1996
(1+2+4+8+.....+512) .(101.102-101.101-50-51) /2+4+6+8+16+....+1024+2048
(1+2+4+8+....+512).(135135.246-246246.135)/2+4+8+16+....+1024+2048
a) 2+4+8+16+32+64+128+256+512+1024+2048
b) \(\frac{\left(2+4+6+8+...+1000\right)nhan10}{2+4+8+16+...+512-2}\)
a)
\(A=2+4+8+...+2048\)
\(A=2+2^2+...+2^{11}\)
\(2A=2^2+2^3+...+2^{12}\)
\(2A-A=\left(2^2+2^3+...+2^{12}\right)-\left(2+2^2+...+2^{11}\right)\)
\(A=2^{12}-2\)
a) 2+4+8+16+32+64+128+512+1024+2048
b thì minh cha ra. Mình sẽ cố làm ra b mong ban thong cam va bạn nho k đung cho minh nha
b)
Xét tử :
( 2 + 4 + 6 + ... + 1000 ) x 10
= 250500 x 10
= 2505000
Xét mẫu :
( 2 + 4 + 8 + ... + 512 ) - 2
Tính như câu a) ta có :
2^10 - 2 - 2
= 2^10 - 4
= 1024 - 4
= 1020
=> TS/MS = 2505000 : 1020 = 41750/17
Vậy,.......
1.Tính hợp lí:
A = \(\frac{\left(1+2+3+...+100\right)x\left(101x102-101x101-50-51\right)}{2+4+8+16...+2048}\)
B = \(\frac{101+100+99+...+3+2+1}{101-100+99-98+...+3-2+1}\)
2. Tìm số tự nhiên x, biết :
a, 697 : \(\frac{15x+364}{x}\)=17
b, 92.4 - 27 = \(\frac{x+350}{x}\)+315
c, 720 : [ 41 - ( 2x -5)] = 40
d, (x+1) + (x+2) +...+ (x+100) = 5750
Lưu ý :
trong bài 2 ko có phép nhân mà là ích-xờ
\(\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{8}\right)+....+\left(1-\frac{1}{512}\right)+\left(1-\frac{1}{1024}\right)\)
\(A=\left[1-\frac{1}{2}\right]+\left[1-\frac{1}{4}\right]+\left[1-\frac{1}{8}\right]+....+\left[1-\frac{1}{512}\right]+\left[1-\frac{1}{1024}\right]\)
\(A=\left(1-\frac{1}{2^1}\right)+\left(1-\frac{1}{2^2}\right)+\left(1-\frac{1}{2^3}\right)+...+\left(1-\frac{1}{2^9}\right)+\left(1-\frac{1}{2^{10}}\right)\)
\(A=\left(1+1+1+...+1+1\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}+\frac{1}{2^{10}}\right)\)
10 số 1
\(A=10-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}+\frac{1}{2^{10}}\right)\)
Đặt \(B=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}+\frac{1}{2^{10}}\)
\(2B=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}+\frac{1}{2^9}\)
\(2B-B=1-\frac{1}{2^{10}}=B\)
=> \(A=10-\left(1-\frac{1}{2^{10}}\right)\)
=> \(A=10-1+\frac{1}{2^{10}}\)
=> \(A=9\frac{1}{1024}\)
Tính :
a) \(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right).\left(1-\frac{1}{15}\right).\left(1-\frac{1}{21}\right)...\left(1-\frac{1}{780}\right)\)
b) \(\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{8}\right)+...+\left(1-\frac{1}{512}\right)+\left(1-\frac{1}{1024}\right)\)
1+1
2+2
4+4
8+8
16+16
32+32
64+64
128+128
256+256
512+512
1024+1024
2048+2048
1+1=2
2+2=4
4+4=8
8+8=16
16+16=32
32+32=64
64+64=128
128+128 = 256
256+256=512
512+512= 1024
1024+1024 = 2048
2048 + 2048 = 4096
1+1=2
2+2=4
4+4=8
8+8=16
16+16=32
32+32=64
64+64=128
128+128=256
256+256=512
512+512=1024
1024+1024=2048
2048+2048=4096
1+1=2
2+2=4
4+4=8
8+8=16
16+16=32
32+32=64
64+64=128
128+128=256
256+256=512
512+512=1024
1024+1024=2048
2048+2048=4096