The sum of the infinite series 1 + 5 6 + 12 6 2 + 22 6 3 + 35 6 4 + 51 6 5 + 70 6 6 + … is equal to:

Step-by-step solution

Given, S = 1 + 5 6 + 12 6 2 + 22 6 3 + 35 6 4 + … . (i) Multiplying with 1 6 both side S 6 = 1 6 + 5 6 2 + 12 6 3 + 22 6 4 + … (ii) On subtraction equation (i) - equation (ii) We get, 5 6 S = 1 + 4 6 + 7 6 2 + 10 6 3 + 13 6 4 + … (iii) Again multiplying 1 6 both side, 5 36 S = 1 + 4 6 2 + 7 6 3 + 10 6 4 + 13 6 5 + . . . (iv) On subtraction equation (iii) - equation (iv) 25 36 S = 1 + 3 6 + 3 6 2 + 3 6 3 + … = 8 5 S = 288 125