Math  /  Calculus

QuestionGiven the series: k=6[1k1k+1]\sum_{k=6}^{\infty}\left[\frac{1}{k}-\frac{1}{k+1}\right] does this series converge or diverge? converges diverges 0
If the series converges, find the sum of the series: k=6[1k1k+1]=\sum_{k=6}^{\infty}\left[\frac{1}{k}-\frac{1}{k+1}\right]= \square (If the series diverges, just leave this second box blank.) Question Help: Video Message instructor

Studdy Solution
Since the series converges, the sum of the series is:
k=6[1k1k+1]=16 \sum_{k=6}^{\infty}\left[\frac{1}{k}-\frac{1}{k+1}\right] = \frac{1}{6}
The series converges, and the sum is:
16 \boxed{\frac{1}{6}}

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