( 10 k + 1 ) = 10 ! ( k + 1 ) ! ( 9 − k ) ! = 10 ! ( 10 − k ) ( k + 1 ) k ! ( 10 − k ) ( 9 − k ) ! = 10 − k k + 1 ( 10 k )
( 10 k ) + ( 10 k + 1 ) = ( 10 − k k + 1 + 1 ) ( 10 k ) = 11 k + 1 ⋅ ( 10 k )
Δ x = a en Δ y = ( 10 k + 1 ) ⋅ ( 1 2 ) 10 − ( 10 k ) ⋅ ( 1 2 ) 10 = ( 10 k ) ⋅ ( 1 2 ) 10 ⋅ ( 10 − k k + 1 − 1 ) = ( 10 k ) ⋅ ( 1 2 ) 10 ⋅ 9 − 2 k k + 1 , dus Δ y Δ x = 1 a ⋅ 9 − 2 k k + 1 ⋅ ( 10 k ) ⋅ ( 1 2 ) 10 Δ y Δ x = 1 a ⋅ 9 − 2 k k + 1 ⋅ ( 10 k ) ⋅ ( 1 2 ) 10
Uit a volgt: 9 − 2 k = ‐ 2 x a , dus Δ y Δ x = 1 a ⋅ 9 − 2 k k + 1 ⋅ ( 10 k ) ⋅ ( 1 2 ) 10 = 1 a ⋅ ( 9 − 2 k ) ⋅ 1 11 ⋅ 11 k + 1 ⋅ ( 10 k ) ⋅ ( 1 2 ) 10 = 1 a ⋅ ‐ 2 x a ⋅ 1 11 ⋅ 2 y = ‐ 4 11 a 2 ⋅ x ⋅ y