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Solution: Evaluating series Evaluate the following infinite
Chapter 1, Problem 15RE(choose chapter or problem)
12-20. Evaluating series Evaluate the following infinite series or state that the series diverges.
\(\sum_{k=1}^{\infty} \frac{1}{k(k+1)}\)
Questions & Answers
QUESTION:
12-20. Evaluating series Evaluate the following infinite series or state that the series diverges.
\(\sum_{k=1}^{\infty} \frac{1}{k(k+1)}\)
ANSWER:STEP_BY_STEP SOLUTION Step-1 Definition ; A series is said to be convergent if it approaches some limit .Formally , the infinite series a n is convergent if the sequence of partial sums n=1 n S n a is convergent . Conversely , a series is divergent if the k=1 ksequence ofpartial sums is divergent.NOTE : The terms grow without bound , so the sequence does not converge. If U k and V k are convergent series , then ( U + k k ) and ( U - Vk k ) areconvergent