Let {x_n}_{n=1}^{\infty}, and {y_n}_{n=1}^{\infty} be two sequences of positive numbers.

Advadlippabrj

Advadlippabrj

Answered question

2022-01-23

Let {xn}n=1, and {yn}n=1 be two sequences of positive numbers. Assume that xnyn
For each one of the following claims, decide whether they are always true, always false, or sometimes true and sometimes false (depending on the specific sequences) and prove it.
1)xnxn+yn2
2)xn+yn2yn

Answer & Explanation

Dominique Green

Dominique Green

Beginner2022-01-24Added 11 answers

Consider
xnyn
xn+xnyn+xn
xn+xn2yn+xn2
xnyn+xn2
xnxn+yn2
Thus, the statement is true
2)Consider
xnyn
xn+ynyn+yn
xn+yn2yn+yn2
xn+yn2yn
Hence, this statement is true

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