Question

Halle el valor de la serie:

S = 1x3+ 2x5+ 3x7+ .............+19x39

Answer 1

Respuesta: Solucion:

S = 1x3 + 2x5 + 3x7 + ........... + 19x39

S = 1x (1 + 2) + 2x (2 + 3) + 3x (3 + 4) + ........ + 19 (19 + 20)

S = (1x1) + (1x2) + (2x2) + (2x3) + (3x3) + (3x4) + ....... +. (19x19) + 19x20

S = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + .... + 19 ^ 2 + (1x2) + (2x3) + (3x4) + ........ + (19x20)

S = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + .... + 19 ^ 2 + 1x (1 + 1) + 2x (2 + 1) + 3x (3 + 1) + .... + 19x (19 + 1)

S = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + .... + 19 ^ 2 + 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + .... + 19 ^ 2 + 1 + 2 + 3 + ..... + 19

S = 2 [1 ^ 2 + 2 ^ 2 + 3 ^ 2 + .... + 19 ^ 2] + 1 + 2 + 3 + ..... + 19

S = 2 [19 (19 + 1) {2 (19) +1} / 6] + [19 (19 + 1) / 2]

S = 2 [19 (20) (39) / 6] + 19 (20) / 2

S = 2 [2470] + 190

S = 4940 + 190

S = 5130

Explicación paso a paso:

Answer 2

Respuesta:

5130

Explicación paso a paso:  

S = 1x3 + 2x5 + 3x7 + ........... + 19x39

S = 1x (1 + 2) + 2x (2 + 3) + 3x (3 + 4) + ........ + 19 (19 + 20)

S = (1x1) + (1x2) + (2x2) + (2x3) + (3x3) + (3x4) + ....... +. (19x19) + 19x20

S = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + .... + 19 ^ 2 + (1x2) + (2x3) + (3x4) + ........ + (19x20)

S = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + .... + 19 ^ 2 + 1x (1 + 1) + 2x (2 + 1) + 3x (3 + 1) + .... + 19x (19 + 1)  

S = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + .... + 19 ^ 2 + 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + .... + 19 ^ 2 + 1 + 2 + 3 + ..... + 19  

S = 2 [1 ^ 2 + 2 ^ 2 + 3 ^ 2 + .... + 19 ^ 2] + 1 + 2 + 3 + ..... + 19  

S = 2 [19 (19 + 1) {2 (19) +1} / 6] + [19 (19 + 1) / 2]

S = 2 [19 (20) (39) / 6] + 19 (20) / 2

S = 2 [2470] + 190

S = 4940 + 190  

S = 5130