Asked by Amy
Determine whether the statement is true or false. Explain your answer.
1. An infinite series converges if its sequence of partial sums is bounded and monotone.
1. An infinite series converges if its sequence of partial sums is bounded and monotone.
Answers
Answered by
oobleck
surely
sin(x) is bounded, but not monotone, so it does not converge.
But if it is bounded and monotone, it must approach the bound arbitrarily closely.
sin(x) is bounded, but not monotone, so it does not converge.
But if it is bounded and monotone, it must approach the bound arbitrarily closely.
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