## Prove that the sequence $a_1, a, a_2, a, a_3, a,\ldots$ converges iff $a_1,a_2,a_3,\ldots$ converges November 28

Prove that the sequence $a_1, g, a_2, g, a_3, g,\ldots$ converges to $g$ iff $a_1,a_2,a_3,\ldots$ converges to $g$.Obviously, if $a_1, g, a_2, g, a_3, g,\ldots$ converges to $g$, then its subsequence $a_1,a_2,a_3,\ldots$ converges to $g$. On the cont