1^64+1^5
LD
Những câu hỏi liên quan
\(\left(\dfrac{1}{64}-\dfrac{1}{3^2}\right).\left(\dfrac{1}{64}-\dfrac{1}{4^2}\right).\left(\dfrac{1}{64}-\dfrac{1}{5^2}\right)...\left(\dfrac{1}{64}-\dfrac{1}{64^2}\right)\)
\(\left(\dfrac{1}{64}-\dfrac{1}{3^2}\right)\left(\dfrac{1}{64}-\dfrac{1}{4^2}\right)...\left(\dfrac{1}{64}-\dfrac{1}{64^2}\right)\)
\(=\left(\dfrac{1}{64}-\dfrac{1}{3^2}\right)\left(\dfrac{1}{64}-\dfrac{1}{4^2}\right)...\left(\dfrac{1}{64}-\dfrac{1}{8^2}\right)...\left(\dfrac{1}{64}-\dfrac{1}{64^2}\right)\)
\(=\left(\dfrac{1}{64}-\dfrac{1}{3^2}\right)\left(\dfrac{1}{64}-\dfrac{1}{4^2}\right)...0...\left(\dfrac{1}{64}-\dfrac{1}{64^2}\right)\)
\(=0\)
Vậy...
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thu gọn:
a) (2+1)(2^2+1)(2^4+1)..............(2^32+1)-2^64
b) (5+3)(5^2+3^2)(5^4+3^4)...................(5^64+3^64).\(\frac{5^{128}-3^{128}}{2}\)
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
1/3 - 3/4 - (-3/5) + 1/64 - 2/9 - 1/36 + 1/5
\(=\left(\dfrac{1}{3}-\dfrac{3}{4}-\dfrac{2}{9}-\dfrac{1}{36}\right)+\left(\dfrac{3}{5}+\dfrac{1}{5}\right)+\dfrac{1}{64}\)
\(=\dfrac{12-9-8-1}{36}+\dfrac{4}{5}+\dfrac{1}{64}\)
\(=\dfrac{-1}{6}+\dfrac{1}{64}+\dfrac{4}{5}=\dfrac{623}{960}\)
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so sánh 12(5^2+1)(5^4+1)(5^8+1)(5^16+1)(5^32+1) và 5^64-1
\(12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{32}-1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{64}-1\right)\)
tính
( 1/3 - 1/7 - 1/13 ) / ( 2/3 - 2/7 - 2/13 ) x ( 3/4 - 3/16 - 3/64 - 3/256 ) / ( 1- 1/4 - 1/16 - 1/64 ) + 5/8
a,1/2*5/4+1/2*3/4+1/2
b,72/95*64/72*95/72*14/86*72/64*86/14
Tính thuận tiện,đây là *nhân nha
a) `1/2 xx 5/4 + 1/2 xx 3/4 + 1/2`
`=1/2 xx (5/4 + 3/4 + 1)`
`=1/2 xx 3`
`=3/2`
b) `72/95 xx 64/72 xx 95/72 xx 14/86 xx 72/64 xx 86/14`
`=(72xx64xx95xx14xx72xx86)/(95xx72xx72xx86xx64xx14)`
`= 1`.
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b)=(72/95.95/72).(64/72.72/64).(14/86.86/14)
=1.1.1=1
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Xem thêm câu trả lời
1/4^2 + 1/5^2 + 1/6^2 + ... + 1/64^2 < 5/16
Ta có: \(\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+...+\frac{1}{64^2}< \frac{1}{4^2}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{63.64}\)
\(\frac{1}{4^2}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{63.64}=\frac{1}{4^2}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{63}-\frac{1}{64}\)
\(=\frac{1}{4^2}+\frac{1}{4}-\frac{1}{64}\)
VÌ: \(\frac{1}{4^2}+\frac{1}{4}-\frac{1}{64}< \frac{1}{4^2}+\frac{1}{4}=\frac{5}{16}\)
Nên: \(\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+...+\frac{1}{64^2}< \frac{5}{16}\left(dpcm\right)\)
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Thu gọn a):\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right).....\left(2^{32}+1\right)-2^{64}\)
b)\(\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{64}+3^{64}\right)+\frac{5^{128}-3^{128}}{2}\)
các pn júp mk nha, mk tik cho, mk cần ngày mai nộp roài
a) (2+1)(2^2+1)(2^4+1)...(2^32+1)-2^64
=(2+1)(2-1)(2^2+1)(2^4+1)...(2^32+1)-2^64
=(2^2-1)(2^2+1)(2^4+1)...(2^32+1)-2^64
=(2^4-1)(2^4+1)....(2^32+1)-2^64
=......
=(2^32-1)(2^32+1)-2^64
=2^64-1-2^64=-1
b)Đặt A=(5+3)(5^2+3^2)(5^4+3^4)...(5^64+3^64)+(5^128-3^128)/2
đặt B=(5+3)(5^2+3^2)(5^4+3^4)...(5^64+3^64)
\(2B=\left(5-3\right)\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{64}+3^{64}\right)\)
\(2B=\left(5^2-3^2\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{64}+3^{64}\right)\)
\(2B=\left(5^4-3^4\right)\left(5^4+3^4\right)...\left(5^{64}+3^{64}\right)\)
\(2B=.......\)
2B=(5^64-3^64)(5^64+3^64)
2B=5^128-3^128
B=(5^128-3^128)/2 (thế vào đề bài)
=> A=B+(5^128-3^128)/2=(5^128-3^128)/2+(5^128-3^128)/2=\(\frac{2\left(5^{128}-3^{128}\right)}{2}=\left(5^{128}-3^{128}\right)\)
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a) A = ( 2-1)(2+1)(22+1)...(232+1)-264
=(22-1)(22+1)(24+1)... -264
=....
=264-1-264=1
câu b tương tự nhá
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