HP49-50G plotting of sum(x=0 to 0, 1, 2,...10, of x!/(2x)!)

[Albert Chan]

(11-05-2023 08:32 PM)Albert Chan Wrote:  \[ \displaystyle \sum_{k=0}^\infty \frac{k!}{(2 k)!}
= 1+\frac{1}{2}
\left(1 + \frac{1}{6}
\left( 1 + \frac{1}{10}
\left( 1 + \frac{1}{14}
\left(1 + \cdots
\right)\right)\right)\right)
\]

\[ \displaystyle \sum_{k=0}^\infty \frac{(k!)^2}{(2 k)!}
= 1+\frac{1}{2}
\left(1 + \frac{2}{6}
\left( 1 + \frac{3}{10}
\left( 1 + \frac{4}{14}
\left(1 + \cdots
\right)\right)\right)\right)
\]

10 K=2 @ D=K @ S=0
20 REPEAT @ DISP 1+S @ S=S+1/D @ K=K+4 @ D=D*K*4/(K+2) @ UNTIL D+1=D
>run
 1
 1.5
 1.66666666667
 1.71666666667
 1.73095238095
 1.73492063492
 1.736002886
 1.73629426129
 1.73637196137
 1.73639252904
 1.73639794158
 1.73639935916
 1.7363998251
 1.73639985003
 1.73639985648
 1.73639985814
 1.73639985857
 1.73639985868
 1.73639985871
 1.73639985872