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first question：

Code:

rsolve(a(n+1)=a(n)^2,a(n),a(1)=1)

XCAS output results：

Quote:"Unable to isolate rsolve_x0 in seqsolve([rsolve_x0^2,[rsolve_x0,n],[rsolve_x0]])"

second question：

Code:

rsolve(a(n+1)=(2*n^2*a(n)+4n*a(n)+2*a(n)+1)/(2n^2+4n-a(n)+2),a(n),a(1)=1/2)

Terminal output：

Quote:Cst part must be hypergeometric
Unable to solve recurrence

The second number of questions can be tried by mathematical methods. Thank you for browsing, Happy New Year.

Section 19.2 (page 304) of Symbolic computation and Mathematics with the calculator HP Prime (hp-prime_cas.pdf) goes into more detail about what forms of sequences are supported by rsolve. This information has been omitted from the official HP Prime User Guide for some reason.

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