MCQ
$\mathop {\lim }\limits_{n \to \infty } \left[ {\frac{1}{{1 - {n^2}}} + \frac{2}{{1 - {n^2}}} + \frac{3}{{1 - {n^2}}} + ........ + \frac{n}{{1 - {n^2}}}} \right] =$
- A$0$
- ✓$ - \frac{1}{2}$
- C$1/2$
- Dએકપણ નહી.
$ = \mathop {\lim }\limits_{n \to \infty } \,\frac{{\Sigma n}}{{1 - {n^2}}} = \frac{1}{2}\,\,\mathop {\lim }\limits_{n \to \infty } \,\,\,\frac{{{n^2} + n}}{{1 - {n^2}}} = - \frac{1}{2}$.
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$x\,\,\cos \,\,\frac{{\alpha + \beta }}{2}\,\, + \,\,y\,\,\sin \,\,\frac{{\alpha + \beta }}{2}\,\, = \,\,$