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7 tháng 10 2017
\(100^2-99^2+98^2-97^2+...+2^2-1\)
\(=\left(100^2-99^2\right)+\left(98^2-97^2\right)+....+\left(2^2-1^2\right)\)
\(=\left(100-99\right)\left(100+99\right)+\left(98-97\right)\left(98+97\right)+....+\left(2-1\right)\left(2+1\right)\)
\(=1.199+1.195+...+1.3\)
\(=199+195+....+3\)
\(=\left[\left(\dfrac{199-3}{4}\right)+1\right]:2.\left(199+3\right)=5050\)
\(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(=4\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(=\dfrac{\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)
\(=\dfrac{\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)
\(=\dfrac{\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)
\(=\dfrac{\left(3^{16}-1\right)\left(3^{16}+1\right)}{2}\)
\(=\dfrac{3^{32}-1}{2}\)
\(3\left(2^2+1\right)\left(2^4+1\right).....\left(2^{64}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{64}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right).....\left(2^{64}+1\right)\)
\(=\left(2^8-1\right)......\left(2^{64}+1\right)=2^{128}-1\)
20 tháng 12 2016
3 (22 + 1)(24 + 1)(28 + 1)(216 + 1)
=(22 - 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)
=(24 - 1)(24 + 1)(28 + 1)(216 + 1)
=(28 - 1)(28 + 1)(216 + 1)
=(216 - 1)(216 + 1)
=232 -1
VM
23 tháng 12 2019
\(3.\left(2^2+1\right).\left(2^4+1\right).\left(2^8+1\right).\left(2^{16}+1\right)\)
\(=\left(2^2-1\right).\left(2^2+1\right).\left(2^4+1\right).\left(2^8+1\right).\left(2^{16}+1\right)\)
\(=\left(2^4-1\right).\left(2^4+1\right).\left(2^8+1\right).\left(2^{16}+1\right)\)
\(=\left(2^8-1\right).\left(2^8+1\right).\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right).\left(2^{16}+1\right)\)
\(=2^{32}-1.\)
Chúc bạn học tốt!
SK
6 tháng 12 2016
3(2^2+1)(2^4+1)(2^8+1)(2^16+1)
=(2^2-1)(2^2+1)(2^4+1).......
=(2^2-1)(2^2+1) là hằng đẳng thức và = (2^4-1)
tương tự cứ như thế kết quả biểu thức là 2^32-1
6 tháng 12 2016
\(A=\left(....\right)\)
3=4-1=(2^2-1)
A.=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)
=(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
KL
A=\(2^{32}-1\)
TT
17 tháng 9 2018
A = 12 – 22 + 32 – 42 + … – 20042 + 20052
A = 1 + (32 – 22) + (52 – 42)+ …+ ( 20052 – 20042)
A = 1 + (3 + 2)(3 – 2) + (5 + 4 )(5 – 4) + … + (2005 + 2004)(2005 – 2004)
A = 1 + 2 + 3 + 4 + 5 + … + 2004 + 2005
A = ( 1 + 2002 ). 2005 : 2 = 2011015
b/ B = (2 + 1)(22 +1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) – 264
B = (22 - 1) (22 +1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) – 264
B = ( 24 – 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) – 264
B = …
B =(232 - 1)(232 + 1) – 264
B = 264 – 1 – 264
B = - 1
TT
17 tháng 9 2018
xin lỗi nha chỗ câu a mình lộn
chỗ (1+2002)x2005:2=2011015 là sai nha
(1+2005)x2005:2= 2011015 là đúng nha
MT
13 tháng 7 2015
như thế này chứ:
A=1002-992+982-972+...+22-12
B=12-22+32-42+...-20082-20092
C=3.(22+1)(24+1)(28+1)(216+1)-232
DN
1
T
7 tháng 10 2015
3(22+1)(24+1)(28+1)(216+1)(232+1)(264+1)
=(22-1)(22+1)(24+1)(28+1)(216+1)(232+1)(264+1)
=(24-1)(24+1)(28+1)(216+1)(232+1)(264+1)
=(28-1)(28+1)(216+1)(232+1)(264+1)
=(216-1)(216+1)(232+1)(264+1)
=(232-1)(232+1)(264+1)
=(264-1)(264+1)
=(2128-1)
Nếu thấy đúng thì thích cho mình nha
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^8-1)(2^8+1)(2^16+1)+1
=(2^16-1)(2^16+1)+1
=2^32-1+1
=2^32
\(3\left(2^2+1\right)\left(2^4+1\right)...\left(2^{16}+1\right)+1\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{16}+1\right)+1\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)+1\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)+1\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)+1\)
\(=\left(2^{32}-1\right)+1\)
\(=2^{32}\)