• # question_answer The value of the sum of the series$3{{\cdot }^{n}}{{C}_{0}}-8{{\cdot }^{n}}{{C}_{1}}+13{{\cdot }^{n}}{{C}_{2}}-18{{\,}^{n}}{{C}_{3}}+...$ A)  0                                 B)  ${{3}^{n}}$ C)  ${{5}^{n}}$                       D)  None of these

The general term of the series is $-h=-u{{t}_{2}}+\frac{1}{2}gt_{2}^{2}$          $0=u({{t}_{2}}-{{t}_{1}})+\frac{1}{2}g(t_{1}^{2}-t_{2}^{2})$ $u=\frac{1}{2}g({{t}_{1}}+{{t}_{2}})$  Sum of the series is given by $h=\frac{g{{t}_{1}}{{t}_{2}}}{2}$ $\sqrt{2}\,mv$ $\sqrt{2}\,mv'=(2m)\,v$ $\Rightarrow$