∑(Un+Vn)肯定发散!
证明:假如∑(Un+Vn)收敛,那么
∑Vn=∑[(Un+Vn)-Un]
=∑(Un+Vn)-∑Un,
∑(Un+Vn)和∑Un都收敛,则它们的差∑Vn也收敛,这是和条件相抵触的,所以假设不成立,∑(Un+Vn)肯定发散!
∑(Un+Vn)肯定发散!
证明:假如∑(Un+Vn)收敛,那么
∑Vn=∑[(Un+Vn)-Un]
=∑(Un+Vn)-∑Un,
∑(Un+Vn)和∑Un都收敛,则它们的差∑Vn也收敛,这是和条件相抵触的,所以假设不成立,∑(Un+Vn)肯定发散!