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The answer is 41.41
Since we know the side that is opposite to a, and the hypotenuse, we have enough information to get the cosine of a. The cosine is 45/60. If we know the cosine of an angle, we can get the arccos of that value to get the angle. The arccos of 45/60 is about 41.41.
Since we know the side that is opposite to a, and the hypotenuse, we have enough information to get the cosine of a. The cosine is 45/60. If we know the cosine of an angle, we can get the arccos of that value to get the angle. The arccos of 45/60 is about 41.41.
a. Notice that
1/(1*2) = 1/2 = 1 - 1/2
1/(2*3) = 1/6 = 1/2 - 1/3
1/(3*4) = 1/12 = 1/3 - 1/4
and so on, which suggests the n-th term of the sum can be written as
Then the sum itself is telescoping:
b. The proof is trivial:
so the formula found in (a) is correct.