A) \[\frac{{{n}^{2}}+n+1}{2}\]
B) \[{{n}^{2}}+n+2\]
C) \[\frac{{{n}^{2}}+n+2}{2}\]
D) \[\frac{{{n}^{2}}+2n+2}{2}\]
Correct Answer: C
Solution :
Let \[S=2+4+7+11+16+........+{{T}_{n}}\] \[S=2+4+7+11+16+........{{T}_{n-1}}+{{T}_{n}}\] Subtracting, we get \[0=2+\left\{ 2+3+4+........+({{T}_{n}}-{{T}_{n-1}}) \right\}-{{T}_{n}}\] \[\Rightarrow \]\[{{T}_{n}}=1+(1+2+3+4+......\text{upto}\ n\ \text{terms})\] \[\Rightarrow \]\[1+\frac{1}{2}n(n+1)=\frac{2+{{n}^{2}}+n}{2}=\frac{{{n}^{2}}+n+2}{2}\].
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