If S_n = 2 + 4 + 7 + 11 + dots + n terms,then | vedclass

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(C) The given series is $S_n = 2 + 4 + 7 + 11 + \dots + t_n$.Let the sequence be $a_n = 2, 4, 7, 11, \dots$.The differences between consecutive terms

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$\frac{n^2 + n + 2}{2}$

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(C) The given series is $S_n = 2 + 4 + 7 + 11 + \dots + t_n$.Let the sequence be $a_n = 2, 4, 7, 11, \dots$.The differences between consecutive terms are $2, 3, 4, \dots$,which form an arithmetic progression.Thus,$t_n = t_1 + \sum_{k=1}^{n-1} (k+1)$.$t_n = 2 + [2 + 3 + 4 + \dots + n]$.This is $t_n = 1 + [1 + 2 + 3 + \dots + n]$.Using the sum formula $\sum_{k=1}^{n} k = \frac{n(n+1)}{2}$,we get:$t_n = 1 + \frac{n(n+1)}{2} = \frac{2 + n^2 + n}{2} = \frac{n^2 + n + 2}{2}$.

If $S_n = 2 + 4 + 7 + 11 + \dots + n$ terms,then $t_n = \dots$

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