tinh:3.(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)
tinh
a,1/2+1/4+1/8+1/16+1/32
b,1/2+1/3+1/6
a) 1/2+1/4+1/8+1/16+1/32
Đặt A = 1/2+1/4+1/8+1/16+1/32
A x 2 = 2 x (1/2+1/4+1/8+1/16+1/32 )
= 1 + 1/2 + 1/4 +1/6
Lấy A x 2 - A ta có :
A x 2 - A = 1 + 1/2+1/4+1/8+1/16+ - 1/2+1/4+1/8+1/16+1/32
A = 1 - 1/32
A = 31/32
Câu b dễ nên tự làm đi
1. tinh nhanh: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
2. tim x: ( x + 1/2 ) + ( x +1/4 ) + ( x + 1/8 ) + ( x + 1/16 ) = 1
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(2\times A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2\times A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\right)\)
\(A=1-\frac{1}{128}\)
\(A=\frac{127}{128}\)
\(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
\(2\times B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\)
\(B=1-\frac{1}{16}=\frac{15}{16}\)
\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(\Leftrightarrow4\times x+\frac{15}{16}=1\)
\(\Leftrightarrow4\times x=\frac{1}{16}\)
\(\Leftrightarrow x=\frac{1}{64}\)
bai 1: Tinh nhanh
a) 1/2 + 1/4 + 1/8 + 1/16 + 1/32
b) 1/2 x 1/2 + 1/2 x 1/3 + 1/3 + 1/3 + 1/4 + 1/4 x 1/5 + 1/5 x 1/6
1.a
1/2+1/4+1/8+1/16+1/32
= 1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32
= 1-1/32=31/32
1b
\(\frac{1}{2}.\frac{1}{2}+\frac{1}{2}.\frac{1}{3} +\frac{1}{3}+\frac{1}{3}+\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{6}+\frac{2}{3}+\frac{1}{4}+\frac{1}{20}+\frac{1}{30}\)
\(=\frac{5}{20}+\frac{5}{30}+\frac{20}{30}+\frac{5}{20}+\frac{1}{20}+\frac{1}{30}\)
\(=\left(\frac{5}{20}+\frac{5}{20}+\frac{1}{20}\right)+\left(\frac{5}{30}+\frac{20}{30}+\frac{1}{30}\right)\)
\(=\frac{11}{20}+\frac{26}{30}\)
\(=\frac{11}{20}+\frac{13}{15}\)
\(=\frac{17}{12}\)
Đó là các cách bạn Võ Thạch Tín đã nêu ra nên mình ko còn câu trả lời nào hết
1*2*4+2*4*8+4*8*16+8*16*32/1*3*4+2*6*8+4*12*16+8*24*32
Tính
1*2*4+2*4*8+4*8*16+8*16*32/1*3*4+2*6*8+4*12*16+8*24*32 = 56744
1*2*4+2*4*8+4*8*16+8*16*32/1*3*4+2*6*8+4*12*16+8*24*32 = 56744
#nhớ tk
tinh nhanh 1/2+1/4+1/8+1/16+1/32+1/64
A x 2 = 1 + 1/2+1/4+1/8+1/16+1/32
A x 2 - A = (1 + 1/2+1/4+1/8+1/16+1/32 ) - ( 1/2+1/4+1/8+1/16+1/32 +1/64)
A = 1 - 1/64
A = 63/64
tinh nhanh :
1/2+1/4+1/8+1/16+1/32=
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=\frac{16}{32}+\frac{8}{32}+\frac{4}{32}+\frac{2}{32}+\frac{1}{32}\)
=\(\frac{16+8+4+2+1}{32}=\frac{31}{32}\)
Tinh bang cach hop li
1/2+1/4+1/8+1/16+1/32
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
=> \(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
=> \(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)
=> \(A=1-\frac{1}{32}=\frac{31}{32}\)
tính nhanh p/s 1+ 5/4 + 5/8 + 5/16 + 5/32 + 5/64
b) 1/3 +1/9 + 1/27 + 1/81 +...........+ 1/59049
c) 3/2 + 3/8 + 3/32 +3/128 + 3/512
d) 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 giúp mình với
b: A=1/3+1/9+...+1/3^10
=>3A=1+1/3+...+1/3^9
=>A*2=1-1/3^10=(3^10-1)/3^10
=>A=(3^10-1)/(2*3^10)
c: C=3/2+3/8+3/32+3/128+3/512
=>4C=6+3/2+...+3/128
=>3C=6-3/512
=>C=1023/512
d: A=1/2+...+1/256
=>2A=1+1/2+...+1/128
=>A=1-1/256=255/256
B=2*4+2*4*8+4*8*16+8*16*32 / 3*4+2*6*8+4*12*16+8*24*32 các bạn có thể giả bằng 1 số nhân với 1 tổng ko ?