Given that:
(1)-4 + (3)-4 + (5)-4 + ... = π4/96
Then, find the value of:
(1)-4 + (2)-4 + (3)-4 + ...
t=vpa(0);
for i=vpa(1):2:2555
t=t+1/i^4;
end
t
pi^4/96
disp(' ')
t2=vpa(0);
for i=vpa(1):2555
t2=t2+1/i^4;
end
t2
pi^4/90
t =
1.0146780315942112381114026078564
ans =
1.01467803160419
shows the first relation holding to about 10 significant figures.
t2 =
1.082323233691164834903103369806
ans =
1.08232323371114
shows Wolfram Alpha's suggestion of pi^4/90 for the second series looking about as good an approximation, and could be the answer.
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Posted by Charlie
on 2023-10-22 09:48:39 |
possible solution
