Question

Halle la suma de cifras de: S = 3x7+5x9+7x11+…..+27x31+29x33

Answer 1

Respuesta:

S = 3710

Explicación paso a paso:

34.

S = 1(1 + 4) + 2(2 + 4) + 3(3 + 4) +......+ 20(20 + 4)

S = 1² + 1×4 + 2² + 2×4 + 3² + 3×4 +......+ 20² + 4×20

S = 1² + 2² + 3² +......+ 20² + 1×4 + 2×4 + 3×4 +.......+ 4×20

S = 1² + 2² + 3² +......+ 20² + 4(1 + 2 + 3 +.......+ 20)

Utilizar:

1² + 2² + 3² +......+ n² = n(n + 1)(2n + 1) / 6

1 + 2 + 3 +.......+ n = n(n + 1) / 2

S = 20(20 + 1)(2(20) + 1) / 6 + 4(20(20 + 1) / 2)

S = 20(21)(40 + 1) / 6 + 2(20(21))

S = 10(7)(41) + 2(420)

S = 10(287) + 840

S = 2870 + 840

S = 3710