Around 1910, the Indian mathematician Srinivasa Ramanujan discovered the formula 1 2/2 (4n)!(1103 + 26390n) - = 9801 (n!)*3964n TT n=0 William Gosper used this series in 1985 to compute the first 17 million digits of T. (a) Verify that the series is convergent.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![to the sum of the series.
(b) Find a value of n so that Sn is within 0.00005 of the sum.
Use this value of n to approximate the sum of the series.
48. Use the sum of the first 10 terms to approximate the sum of
the series
Σ
2"
noiteupo ors ved viovieen
Use Exercise 46 to estimate the error.
n=1
49. Prove the Root Test. [Hint for part (i): Take any number r such
that L <r< 1 and use the fact that there is an integer N such
that an < r whenever n >N.]
ortiodw onimoto
50. Around 1910, the Indian mathematician Srinivasa Ramanujan
discovered the formula
1
2/2
(4n)!(1103 + 26390n)
9801
(n!)43964n
TT
n=0
William Gosper used this series in 1985 to compute the first
17 million digits of T.
(a)Verify that the series is convergent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2195755-482e-43b2-9535-9be7e3b0c44a%2F5781bc18-0136-43a0-b0e9-1451d1c74020%2F33gcy93_processed.jpeg&w=3840&q=75)
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