Let $\displaystyle (x^{(n)})^\infty_{n=1}= ((x_k^{(n)})_{k=1}^{\infty})_{n=1}^{\infty} $be a sequence of elements of $\displaystyle l_1$. Prove that if $\displaystyle (x^{(n)})_{n=1}^{\infty}$ converges in $\displaystyle l_1$ to $\displaystyle x=(x_k)_{k=1}^{\infty}$, then for every $\displaystyle K \in N$, the sequence $\displaystyle (x_k^{(n)})_{n=1}^{\infty}$ converges in $\displaystyle R$ to $\displaystyle x_k$. Show by example that the converse is not true.