Consider the series ++++ + .. .... Does the series converge or diverge?

Q: ハ-1 に2

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Q: The series (an - an+1) converges iff the sequence an converges. (Tips: Cauchy Criterion for Series)

A: We have to prove that, the series ∑n=1∞an−an+1 converges if and only if the sequence an converges.…

Q: Find the sum of n terms of the series 1.24 +2.3 +3.4 +..

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Q: Consider the series (k!)³ (3k)! k=0 Determine if the series converges or diverges.

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Q: 7 + 10 + 13 + . + 40 i-

A: 7+10+13+....+40  First term⇒ a1=7, Last term⇒ an=40common differnce⇒10-7=3 Last term=First…

Q: (n*+3n)" (4n +5)"

A: Use Cauchy's root test

Q: 8 n=1 5n. (n!)² (2n)!. 4n

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Q: Converges (by geometric series)

A: If  the geometric series is given by: ∑n=0∞arn=a+ar+ar2+..... If r<1 then geometric series…

Q: The geometric series 4 5-2+ 5 16 + 25 8 32 125 625 is convergent. true false

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Q: Use the Monotonic Sequence Theorem to show that the sequence n 3n is convergent.

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Q: Is the sequence divergent or convergent? {vn - vn+1}

A: n  - n+1 =(n  - n+1) (n  +n+1 )/(n  + n+1) n  - n+1  = (n - n - 1)/(n  + n+1)  n  - n+1  =  - 1/(n…

Q: Evaluate the telescoping series or state whether the series diverges. (If the quantity diverges,…

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