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prog

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can you help me with my homework

1 2023-10-19 12:14

(2007+1)^(2007-1)*(2007-1)^(2007+1) ? 2007(2*2007)

^-power
*-multiplying
instead of question mark put > or <

2 2023-10-19 12:21

please

3 2023-10-19 14:39

2007(2*2007)

Is this supposed to be 2007^(2*2007)?

4 2023-10-19 14:46

RHS = 2007^(2*2007)
LHS = (2007+1)^(2007-1)*(2007-1)^(2007+1)
(2007 + 1) * LHS / (2007 - 1) = (2007+1)^(2007)*(2007-1)^(2007)
                              = ((2007+1) * (2007-1))^(2007)
                              = ((2007^2) - 1)^2007

Notice that (2007 + 1) * LHS / (2007 - 1) is <= than LHS + 1
but ((2007^2) - 1)^2007 is much smaller than RHS

5 2023-10-19 14:55

Actually it simply becomes:

LHS < (2007 + 1) * LHS / (2007 - 1) = ((2007^2)-1)^2007 < (2007^2)^2007 = RHS

6 2023-10-20 04:45

so the right side is bigger?

7 2023-10-20 04:46

>>3 yes

8 2023-10-20 09:59

>>6
yes

9 2023-10-22 23:38

>>1
Use Macsyma to solve your math problems.

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