Multiple choice

The sum of the series $\displaystyle 1+\frac{9}{4}+\frac{36}{9}+\frac{100}{16}+\cdots$ upto $n$ terms if $n=16$ is

  1. $446$
  2. $746$
  3. $546$
  4. $846$
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A Correct answer
Explanation

The series is 1 + 9/4 + 36/9 + 100/16 + ... which simplifies to 1 + (3/2)^2 + (6/3)^2 + (10/4)^2 + ... The general term is (n(n+1)/2 / n)^2 = ((n+1)/2)^2. Summing this for n=1 to 16 gives the result 446.

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