We knpw that S1=201.
Now by looking at the formula,we can choose to ignore the fraction part as it will tend to zero.
So the question basically translates to S1+1+S2+1+....
Now, S2=S1+1 (The fraction part is ignored as mentioned earlier)
Therefore, S2=202.
Similarly S3=203;S4=204 and so on.
Therefore S50=250
Hence S1+S2+S3+...+S50 will be 201+202+203+...+250 which is 11275.
Hence the answer is (c)

(C) 11,000 < Q < 12,000 i think

SUm of Sn = sum of AP + sum HP ....

Answer

To find each successive term in S, we add 1 to the previous term and add this to the reciprocal of the previous term plus 1.

S1= 201





The question asks to estimate (Q), the sum of the first 50 terms of S. If we look at the endpoints of the intervals in the answer choices, we see have quite a bit of leeway as far as our estimation is concerned. In fact, we can simply ignore the fractional portion of each term. Let’s use S2 &#8776; 202, S3 &#8776; 203. In this way, the sum of the first 50 terms of S will be approximately equal to the sum of the fifty consecutive integers 201, 202 … 250.

To find the sum of the 50 consecutive integers, we can multiply the mean of the integers by the number of integers since average = sum / (number of terms).

The mean of these 50 integers = (201 + 250) / 2 = 225.5

Therefore, the sum of these 50 integers = 50 x 225.5 = 11,275, which falls between 11,000 and 12,000. The correct answer is C.
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