(12C Platinum) Sums of Powers of N numbers

[Thomas Klemm]

We can also use Neville's algorithm to interpolate the polynomial at \(n=10\):

\(\begin{matrix}
0 & 0 & & & & \\
& & 10 & & & \\
1 & 1 & & 325 & & \\
& & 73 & & 1765 & \\
2 & 9 & & 757 & & 3025\\
& & 225 & & 2269 & \\
3 & 36 & & 1261 & & \\
& & 484 & & & \\
4 & 100 & & & &
\end{matrix}\)

For this we can use the HP-12C since only linear forecasts are used:

CLEAR ∑
0 ENTER 0 ∑+
1 ENTER 1 ∑+
10 ŷ,r
10.0000

CLEAR ∑
1 ENTER 1 ∑+
9 ENTER 2 ∑+
10 ŷ,r
73.0000

CLEAR ∑
9 ENTER 2 ∑+
36 ENTER 3 ∑+
10 ŷ,r
225.0000

CLEAR ∑
36 ENTER 3 ∑+
100 ENTER 4 ∑+
10 ŷ,r
484.0000

---

CLEAR ∑
10 ENTER 0 ∑+
73 ENTER 2 ∑+
10 ŷ,r
325.0000

CLEAR ∑
73 ENTER 1 ∑+
225 ENTER 3 ∑+
10 ŷ,r
757.0000

CLEAR ∑
225 ENTER 2 ∑+
484 ENTER 4 ∑+
10 ŷ,r
1261.0000

---

CLEAR ∑
325 ENTER 0 ∑+
757 ENTER 3 ∑+
10 ŷ,r
1765.0000

CLEAR ∑
757 ENTER 1 ∑+
1261 ENTER 4 ∑+
10 ŷ,r
2269.0000

---

CLEAR ∑
1765 ENTER 0 ∑+
2269 ENTER 4 ∑+
10 ŷ,r
3025.0000


Cheers
Thomas