Around 1910 , the Indian mathematician Srinivasa Ramanujan discovered the formula\[\frac{1}{\pi}-\frac{2 \sqrt{2}}{9801} \sum_{n=0}^{=} \frac{(4 n) !(1103+26390 n)}{(n !)^{4} 396^{4 n}}\]William Gosper used this series in 1985 to compute the first17 million digits of $\pi$(a) Verify that the series is convergent.(b) How many correct decimal places of $\pi$ do you get if you use just the first term of the series? What if you use two terms?

Q: find the first 10 terms of the sequence a^n =1/a^n-1 and a^1 = 6 9th term ______ 10th term ______

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Q: What is the generating function for the sequence {ck},where ck represents the number of ways to make…

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Q: [n^2cos(n/2)] / 2n^2 +1 does this sequence converge or diverge & w

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Q: Find the limit of the sequence when the nth term is given.  a sub n = 3^n+2/5n

A: The solution are next step

Q: Will this sequence coverage?  an=(-1^n)n/(n^2-6)

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Q: a_{n}=\frac{(-3)^{n}}{n !}

A: Tn = (-3)n / n! Tn+1 = (-3)n+1 / (n+1)! Tn+1 / Tn = (-3) / (n + 1)

Q: Prove that this sequence is monotonic: an = cot-n

A: ANSWER

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A: Given: A=∫0π2∫01r2+1rdrdθ   To Solve: The given integral.

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Q: Use limit comparison test for sum of n=1 to ♾ of (3n^3+2)^(1/2)/(8n^2+9n+1)

A: take bn = 1/n  we know that if limn→∞anbn= finite  then by limit comparison test both series behave…

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Q: the repeating decimal can be written as a geometric series Σar^k  0.555555555...  what is the value…

A: Given