hi again,can u help me to show
if X(2n) and X(2n+1) convergence to 'a',then show X(n) convergence to 'a'.
If $\displaystyle \varepsilon > 0$ then from the given $\displaystyle \left[ {\exists N_1 }{n \geqslant N_1 \Rightarrow \quad \left| {a_{2n} - a} \right| < \varepsilon } \right]\,\& \,\left( {\exists N_2 } \right)\left[ {n \geqslant N_2 \Rightarrow \quad \left| {a_{2n + 1} - a} \right| < \varepsilon } \right]$.
So if $\displaystyle k \geqslant N_1 + N_2$ then $\displaystyle k$ is either even or odd so in eith case $\displaystyle {\left| {a_k - a} \right| < \varepsilon }$