# Problem. If is a bounded sequence in an inner product space, and is a sequence converging to zero, prove that . Note, here < , > is the inner product notation. Hint: Use triangle inequality.

Problem: If is a bounded sequence in an inner product space, and is a sequence converging to zero, prove that (see attachment).

Note, here < , > is the inner product notation. Hint: Use triangle inequality.

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#### Solution Summary

This solution is comprised of a detailed explanation to prove an inner product space.

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