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Differentiation to Solve Modified Sum of Binomial Coefficients

If the nth ...

Question

If the $n^{t h}$ term of the series is $T_{n} = 2 n - 1$ , then sum of $n$ terms $S_{n}$ will be

n^{2}

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\frac{n (n + 1)}{2}

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\frac{n (n + 1) (n + 2)}{6}

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n + 2

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Solution

The correct option is A $n^{2}$
Here $T_{n} = 2 n - 1$
Thus, Sum, $S_{n} = \sum T_{n} = 2 \sum n - \sum 1 = 2 \frac{n (n + 1)}{2} - n = n^{2}$
Hence, option 'A' is correct.

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