3(2^2+1)(2^4+1)(2^8+1)(2^16+1) = ?
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rút gọn biểu thức
a) A=16^8 -1/(2+1)(2^2+1)(2^4+1)(2^8+1(3^16+1)
b) B=(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/9^16-1
giúp mk vs ah mk đang cần gấp ah
a) Ta có: \(A=\dfrac{16^8-1}{\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^{16}-1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{2^{32}-1}=1\)
b) Ta có: \(B=\dfrac{\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{9^{16}-1}\)
\(=\dfrac{\left(3^2-1\right)\cdot\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\cdot\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\cdot\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^{16}-1\right)\left(3^{16}+1\right)}{2\left(3^{32}-1\right)}=\dfrac{1}{2}\)
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\(\text{ 3(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)}\) 3(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^16 + 1)
Tính nhanh
C=50^2-49^2+48^2-47^2+...+2^2-1^2
D=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)
E=(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
c;=(50-49)(50+49)+(48-47)(48+47)+.............+(2+1)(2-1)
=50+49+48+............+1
=(50+1)50=2550:2=1275
d;=(2^4-1)(2^4+1)(2^8+1)(2^16+1)
=(2^8-1)(2^8+1)(2^16+1)
=(2^16-1)(2^16+1)
=2^32-1
e;=(3-1)(3+1)(3^2+1)...........(3^16+1)
=(3^2-1)(3^2+1)..............(3^16+1)
=(3^16-1)(3^16+1)=3^32-1
tu tinh ket qua luy thua tao khong thua hoi dau
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A3(23+1)(24+1)(28+1)(216+1)
A(22−1).9(24+1)(28+1)(216+1)
Afrac{9}{3}.(22−1)(22+1)(24+1)(28+1)(216+1)
Afrac{9}{3}.(24−1)(24+1)(28+1)(216+1)
Afrac{9}{3}.(28−1)(28+1)(216+1)
Afrac{9}{5}.(216−1)(216+1)
Afrac{9}{3}.(232−1)
các bạn kiểm tra xem mình có đúng ko nhá.............
Đọc tiếp
A=3(23+1)(24+1)(28+1)(216+1)
A=(22−1).9(24+1)(28+1)(216+1)
A=\(\frac{9}{3}\).(22−1)(22+1)(24+1)(28+1)(216+1)
A=\(\frac{9}{3}\).(24−1)(24+1)(28+1)(216+1)
A=\(\frac{9}{3}\).(28−1)(28+1)(216+1)
A=\(\frac{9}{5}\).(216−1)(216+1)
A=\(\frac{9}{3}\).(232−1)
các bạn kiểm tra xem mình có đúng ko nhá.............
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
Xem thêm câu trả lời
bài 1:
1/4 + 2/3 2/7 + 2/3 2/5 + 1/3 2/3 + 1/2 1/3 + 3/5 4/5 + 1/3
1/8 + 3/4 1/36 + 5/12 1/3 + 1/6 + 1/18.
bài 2:
15/16 - 3/16 17/18 - 5/6 3/4 - 4/9 1/2 - 2/5 5/6 - 3/10 3-1/3
4/5 - 1/10 5/2 - 1 5/8 - 2/5.
1/3-1/7-1/13/2/3-2/7-2/3×3/4-3/16-3/64/1-1/4-1/16-1/64+5/8
chứng tỏ rằng
b= 1/2^2+1/3^2+1/4^2+1/5^2+1/6^2+1/7^2+1/8^2<1
b tính nhanh
A= 1+1/2(1+2) +1/3(1+2+3)+1/4(1+2+3+4)+...+ 1/16(1+2+3+...+16)
b)Ta có:\(A=1+\frac{1}{2.\left(1+2\right)}+\frac{1}{3.\left(1+2+3\right)}+...+\frac{1}{16.\left(1+2+3+...+16\right)}\)
\(=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+...+\frac{1}{16}.\left(1+2+3+...+16\right)\)
\(=1+\frac{1}{2}.3+\frac{1}{3}.6+...+\frac{1}{16}.136\)
\(=1+1,5+2+...+8,5\)
\(=\frac{\left(8,5+1\right).\left[\left(8,5-1\right):0,5+1\right]}{2}=76\)
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B=\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}<\)
B=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
B=\(1-\frac{1}{8}=\frac{8}{8}-\frac{7}{8}=\frac{1}{8}<2\)
Vậy 1/8<2 hay 1/8<16/8
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a) chứng tỏ rằng: B= 1/2^2+ 1/3^2 + 1/4^2 + 1/5^2 +1/6^2 + 1/7^2+ 1/8^2<1
b) A= 1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+...+1/16(1+2+3+.....+16)
Ai nhanh mk tick
A = 1/2^2 + 1/3^2 +.. + 1/8^2 < 1/1.2 + 1/2.3 +... + 1/7.8 = 1 - 1/2 + 1/2 -1/3 +... + 1/7 - 1/8
= 1 - 1/8 < 1
\(\Rightarrowđpcm\)
\(tíchnhaminhftchlaij\)
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Chưng tỏ
a, S= 1/2^2+1/3^2+...+1/9^2
Chứng tỏ 2/5<S<8/9
b, 1/2-1/4+1/8-1/16+1/32-1/64<1/3
c, 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16