ssccglapex

(1) + (1 + 1) + (1 + 1 + 1) + ……. + (1 + 1 + 1 + …… n – 1 times) = ……

A. $\Large\frac{n(n+1)}{2}$ B. $\Large\frac{n(n-1)}{2}$ C. $\boldsymbol{n}^{\mathbf{2}}$ D. n Answer: Option B
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Solution(By Apex Team)

$\begin{aligned}S_{n}=[2 a+(n-1) d] \times \frac{n}{2}\end{aligned}$ $\begin{array}{l}\text{Here,}\\ \text{d}=1\\ \text{a}=1\\ \text{and}\ n-1\ \text{terms}\\ \begin{aligned} \Rightarrow S_{n-1} &=[2+(n-1-1)] \times \frac{(n-1)}{2} \\ \Rightarrow S_{n-1} &=[2+n-2] \times \frac{(n-1)}{2} \\ &=\frac{n(n-1)}{2} \end{aligned}\end{array}$

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