The sum of 50 terms of the series `1+2(1+1/(50))+3(1+1/(50))^2+` is given by `2500` b. `2550` c. `2450` d. none of these

Explanation

To find the sum of the first 50 terms of the series given by:

\[ S = 1 + 2\left(1 + \frac{1}{50}\right) + 3\left(1 + \frac{1}{50}\right)^2 + \ldots \]

we can follow these steps:

### Step 1: Define Variables
Let \( n = 50 \) and \( x = 1 + \frac{1}{n} = 1 + \frac{1}{50} = \frac{51}{50} \).
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