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The steps to solve the problem are as follows:
1+1 2 to the 8th power) (1+1 2 to the 4th power) (1+1 2 to the 2nd power) (1+1 2).
1+1 2 to the 8th power) (1+1 2 to the 4th power) (1+1 2 to the 2nd power) (1+1 2) (1-1 2) (1-1 2).
1-1 2 to the 16th power) (1-1 2).
2-1 2 to the 15th power.
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It is like this (1+1 2 to the 8th power) (1+1 2 to the 4th power) (1+1 2 to the 2nd power) (1+1 2).
1+1 2 to the 8th power) (1+1 2 to the 4th power) (1+1 2 to the 2nd power) (1+1 2) (1-1 2) (1-1 2).
1-1 2 to the 16th power) (1-1 2).
2-1 2 to the 15th power.
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1+1 2 to the 8th power) (1+1 2 to the 4th power) (1+1 2 to the 2nd power) (1+1 2).
1+1 2 to the 8th power) (1+1 2 to the 4th power) (1+1 2 to the 2nd power) (1+1 2) (1-1 2) (1-1 2).
1-1 2 to the 16th power) (1-1 2).
2-1 2 to the 15th power.
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The numerator and denominator are multiplied by (1-1, 2) respectively
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(5 + 1) (5 + 1) (5 to the fourth power + 1) (5 to the eighth power + 1) (5 to the 16th power + 1) +
Multiply the first term by (5-1) 4;Since the value is 1, multiplying this item does not affect the result.
Original = [(5-1) (5+1) (5 +1) (5 to the fourth power + 1) (5 to the eighth power + 1) (5 to the 16th power + 1)] 4 + 1 4
5 -1) (5 +1) (5 to the fourth power + 1) (5 to the eighth power + 1) (5 to the 16th power +1)] 4 + 1 4
5 to the fourth power -1) (5 to the fourth power + 1) (5 to the eighth power + 1) (5 to the 16th power +1)] 4 + 1 4
5 to the power of 32 -1) 4 + 1 4
5 to the power of 32 4+1 4-1 4
5 to the 32nd power 4
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(2+1) (2 +1) (2 to the fourth power + 1) (2 to the eighth power + 1)....(2 to the power of 512 +1).
2-1) (2 + 1) (2 + 1) (2 to the fourth power + 1) (2 to the eighth power + 1) ...(2 to the power of 512 +1).
(2+1) (2 +1) (2 to the fourth power + 1) (2 to the eighth power + 1)....(2 to the power of 512 +1).
2 to the fourth power - 1) (2 to the fourth power + 1) (2 to the eighth power + 1) ...(2 to the power of 512 +1).
= (2 to the power of 512 - 1) (2 to the power of 512 + 1).
2 to the power of 1024-1
Happy learning!
o(∩_o~
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Preceded by (2-1) a square difference.
Original = (2-1) (2+1)· (2 +1)· (2 to the fourth power +1) · (2 to the eighth power + 1).
(2+1) (2 +1) (2 to the fourth power + 1) (2 to the eighth power + 1)....
2 to the fourth power -1) (2 to the fourth power +1) · (2 to the eighth power + 1) = (2 to the eighth power - 1) (2 to the eighth power + 1).
2 to the 16th power - 1
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Multiply by (2-1).
2+1) (2 +1) (2 to the power of 4 +1) (2 to the power of 8 +1) +1
2-1) (2 + 1) (2 squared + 1) (2 to the 4th power + 1) (2 to the 8th power + 1) + 1
2 to the 8th power - 1+1
2 to the 16th power.
If it helps you, please remember to adopt, o( o thank you.
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Because (2-1) = 1
So the original formula = (2-1) (2 + 1) (2 + 1) (2 to the fourth power + 1) (2 to the eighth power + 1) ......2 to the nth power +1).
(2+1) (2 +1) (2 to the fourth power + 1) (2 to the eighth power + 1)....2 to the nth power +1).
…= (2 to the nth power - 1) (2 to the n power + 1) = 2 to the n + 1 power - 1
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The title should read: (2 + 1) (2 + 1) (2 to the fourth power + 1) (2 to the eighth power + 1) ......2 to the nth power + 1) [n = 2 m, m is a natural number] (2 + 1) (2 + 1) (2 to the fourth power + 1) (2 to the eighth power + 1) ......2 to the nth power +1).
2-1) (2 + 1) (2 + 1) (2 to the fourth power + 1) (2 to the eighth power + 1) ...2 to the nth power +1).
(2+1) (2 +1) (2 to the fourth power + 1) (2 to the eighth power + 1)....2 to the nth power +1).
2 to the 2n power - 1
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(2+1) (2 +1) (2 to the fourth power + 1) (2 to the eighth power + 1)....2 to the nth power +1).
2-1) (2 + 1) (2 + 1) (2 to the fourth power + 1) (2 to the eighth power + 1) ...2 to the nth power +1).
(2+1) (2 +1) (2 to the fourth power + 1) (2 to the eighth power + 1)....2 to the nth power +1).
2 to the nth power +1).
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(2+1) (2 +1) (2 to the fourth power + 1) (2 to the eighth power + 1)....2 to the nth power +1).
2^-1)(2^2+1)(2^4+1)(2^8+1)..2^n+1)
2^4-1)(2^4+1)(2^8+1)..2^n+1)
2^8-1)(2^8+1)..2^n+1)=2^(2n)-1
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1/2=1-1/2
1 2 + (1 2) +1 2) = 7 8 = 1-1 81 2 + (1 2) +1 2) +1 2) to the power of 4 = 15 16 = 1-1 16 .........1 2 + (1 2) +1 2) +1 2) +1 2).1 2) to the nth power = 1-1 2 to the nth power.
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This is a proportional series, and the common ratio is 1 2
Original 1 2*(1-(1 2) n) (1-1 2).
1-1/2^n
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(1+2) (1+2 ) (1+2 to the fourth power) (1+2 to the eighth power) = -(1-2) (1+2) (1+2) (1+2 to the fourth power) (1+2 to the eighth power).
(1-2) (1+2) (1+2 to the fourth power) (1+2 to the eighth power) = - (1-2 to the fourth power) (1+2 to the fourth power) (1+2 to the eighth power) = - (1-2 to the eighth power) (1+2 to the eighth power).
(1-2 to the sixteenth power).
2 to the sixteenth power - 1
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