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sweet-ann [11.9K]
4 years ago
15

Determine whether the series is convergent or divergent by expressing Sn as a telescopic sum (as in example 7). If it is converg

ent, calculate its sum

Mathematics
1 answer:
blagie [28]4 years ago
4 0

Answer:

Convergent

cos 1 − 1

Step-by-step explanation:

∑ (cos 1/n² − cos 1/(n+1)²)

= lim(n→∞) [(cos 1 − cos 1/4) + (cos 1/4 − cos 1/9) + ... + (cos 1/n² − cos 1/(n+1)²)]

= lim(n→∞) [cos 1 − cos 1/(n+1)²]

= cos 1 − cos 0

= cos 1 − 1

The series converges to cos 1 − 1.

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