OFFSET
1,2
COMMENTS
Ramanujan's question 1070 (i) asks for a proof of the identities
sqrt((1/5)^(1/5)+(4/5)^(1/5)) = (1+2^(1/5)+8^(1/5))^(1/5) = (16/125)^(1/5)+(8/125)^(1/5)+(2/125)^(1/5)-(1/125)^(1/5).
REFERENCES
S. Ramanujan, Coll. Papers, Chelsea, 1962, page 334, Question 1070.
EXAMPLE
1.296584807665018307492401645829135777485135213485302261427431418...
MATHEMATICA
RealDigits[Sqrt[Surd[1/5, 5]+Surd[4/5, 5]], 10, 120][[1]] (* Harvey P. Dale, Dec 14 2021 *)
PROG
(PARI) sqrt((1/5)^(1/5)+(4/5)^(1/5))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Aug 28 2018
STATUS
approved