Use the ratio test to show that the series is convergent.

Thank you!

Step-by-step explanation:

lim(n→∞) |aₙ₊₁ / aₙ|

lim(n→∞) | (4ⁿ⁺¹ / (n+1)!) / (4ⁿ / n!) |

lim(n→∞) | (4ⁿ⁺¹ / (n+1)!) × (n! / 4ⁿ) |

lim(n→∞) | 4 / (n+1) |

0

Since the limit is less than 1, the series converges.

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92