Question

Q. show that if X and Y are sequences such that X and X+Y are convergent, then Y is convergent.

Answer 1

Answer on Question #64523 – Math – Real Analysis

Question

Show that if X and Y are sequences such that X and X+Y are convergent, then Y is convergent.

Solution

We can write $Y = (X + Y) - X$. Then we use two facts:

1) both sequences $X$ and $X + Y$ are convergent

2) the difference of two convergent sequences is also convergent.

Therefore sequence $Y$ is convergent.

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