01-22-2019, 10:20 AM
ALG program solution of "Sums of Powers of the Natural Numbers"
1. Arithmetic Series ( Gauss Sum )
n(n+1) / 2
2. Sum of the consecutive Squares.
n(n+1)(2n+1) / 6
3. Sum of the consecutive Cubes.
n^2(n+1)^2 / 4
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Procedure:
Nth [R/S] display Sums of Powers
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1. Gauss Sum
2. Sums of consecutive Squares
3. Sums of consecutive Cubes
Gamo
1. Arithmetic Series ( Gauss Sum )
n(n+1) / 2
2. Sum of the consecutive Squares.
n(n+1)(2n+1) / 6
3. Sum of the consecutive Cubes.
n^2(n+1)^2 / 4
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Procedure:
Nth [R/S] display Sums of Powers
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1. Gauss Sum
Code:
1 [+] [X<>Y] [x] [LSTx] [÷] 2 [=]
2. Sums of consecutive Squares
Code:
1 [+] [X<>Y] [x] [LSTx] [x] ( [LSTx] [x] 2 [+] 1 ) [÷] 6 [=]
3. Sums of consecutive Cubes
Code:
1 [+] [X<>Y] [=] [X^2] [x] [LSTx] [X^2] [÷] 4 [=]
Gamo