Find the largest positive integer k possible in the following expression, n >= 0
((√2)1+(√2)2)*((√2)3+(√2)4)*...*((√2)2019+(√2)2020) = 2k + n
It would appear to be 511334, which is the truncated (i.e., integer part) of the base-2 logarithm of the given product on the LHS.
4 kill "2manyrts.txt":open "2manyrts.txt" for output as #2
5 point 20
10 Sr2=sqrt(2):L2=log(2)
20 for First=1 to 2019 step 2
30 Fctr=Sr2^First+Sr2^(First+1)
40 Tot=Tot+log(Fctr)/L2
50 print First,Tot
60 next
70 print #2,Tot
80 close #2
The file output is the base-2 log of the LHS:
511334.26883619524809237004849354997890418828482963785991627526969
5108191698252338906400265749178427037
Running with higher precision shows
511334.26883619524809237004849354997890418828482963785991627526969
510819169825233890640026574917853667276291555925708390581132661578
5932879169868971308
indicating a loss of 6 digits of precision (the last six digits of the first given value are wrong).
Edited on March 14, 2019, 3:56 pm
|
|
Posted by Charlie
on 2019-03-14 15:54:56 |
solution
