To simplify the expression, we can first combine the terms in the first set of parentheses:

M = (1/2x^3 + 1/3x^4 + 1/4x^5 + 1/5x^6 + 1/6x^7 + 1/7x^8 + 1/8x^9 + ... + 1/50x^51)

Next, we can simplify the second set of parentheses:

(5/6 + 19/20 + 41/42 + 71/72 + .... + 2549/2550)

To simplify this series, we can see that each term is the sum of consecutive odd numbers starting from 1. Therefore, the series can be written as:

5/6 + (1+18)/20 + (19+22)/42 + (41+30)/72 + .... + (2549+2)/2550

Now, we can simplify each term in the series:

5/6 + 19/20 + 41/42 + 71/72 + .... + 2551/2550

Finally, we can add the two simplified expressions together to get the final result for M.