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Series Calculator


Series Calculator computes sum of a series over the given interval. It is capable of computing sums over finite, infinite and parameterized sequences. For the finite sums series calculator computes the answer quite literally, so if there is a necessity to obtain a short expression we recommend computing a parameterized sum. The Infinite Series Calculator an online tool, which shows Infinite Series for the given input.

How to Use Series Calculator

Necessary condition for a numerical sequence convergence is that limit of common term of series is equal to zero, when the variable approaches infinity. However, this condition is not sufficient to determine the convergence of numerical series online. For series convergence determination a variety of sufficient criterions of convergence or divergence of a series have been found. If an input is given then it can easily show the result for the given number. A special place among numeric series is occupied by such in which the signs of the summands being strictly alternated, and absolute values of the numeric series monotonously subside.

 

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— Jo Morgan (@mathsjem) 6 июня 2019 г.

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It is just a series of logic gates.
Therefore, I repeat, if it doesn’t believe in god, or christ, how can it calculate, in your opinion?

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29 Responses to Series Calculator

  1. Mary D. Iser says:
    May 11, 2019 at 4:15 pm

    What is sum of (5^n*x^(2n))/(6^(n+1)) from n=0 to infinity

    Reply
    • mathmathmath says:
      May 12, 2019 at 4:25 pm

      This series is convergent not for all x.

      Reply
  2. Dillon says:
    June 19, 2019 at 4:17 pm

    Find exact sum:
    Summation(1/(n^2) – 1/(n+3)^2), n=1 to infinity
    Can you show the steps please?

    Reply
    • mathmathmath says:
      June 19, 2019 at 7:27 pm

      Write out a few terms: (1/1^2-1/4^2)+(1/2^2-1/5^2)+(1/3^2-1/6^2)+(1/4^2-1/7^2) + …
      As you can see most terms are cancelled out and you’re left only with 1/1^2 + 1/2^2 + 1/3^2 = 49/36

      Reply
  3. Ide says:
    June 29, 2019 at 4:16 pm

    from 1 to infinity sum of 4/(k+2)^2 Gotta find if it converges. Im kinda lost

    Reply
    • mathmathmath says:
      June 30, 2019 at 11:26 am

      It converges.

      Reply
  4. Fermin Aarestad says:
    July 2, 2019 at 12:15 pm

    Thanks for The Calculator , Nice Website

    Reply
  5. Sylvia R says:
    July 21, 2019 at 4:15 pm

    Find if this series converges for 1 to inf: (-1)^n tan^-1 ((n+sin(n!)) / (n^2+sin(n!)^2))?

    Reply
    • mathmathmath says:
      July 21, 2019 at 11:25 pm

      This series is hard to find.

      Reply
  6. Gwendolyn says:
    August 2, 2019 at 4:14 pm

    binomial(2n,n)x^n from 0 to infinity=(1-4x)^-1/2 now put x=-1/16

    Reply
    • mathmathmath says:
      August 2, 2019 at 7:24 pm

      If x = -1/16, then binomial(2n,n)(-1/16)^n from 0 to infinity=(1-4(-1/16))^-1/2 = (1+1/4)^(-1/2)=(5/4)^(-1/2)=(4/5)^(1/2)=2/sqrt(5)

      Reply
  7. Toccara says:
    August 4, 2019 at 4:16 pm

    Your calculators were great but the advertisements you have are unbearable. Every time I click calculate, an ad pops up, and you have an ad on the bottom right corner that blocks the solutions. When I try to close it, another ad pops up. I literally get 7 ads that open up in new tabs for each time I use the calculator.

    The way you had it before was great, you still had advertisements but it did not prevent me/us from calculating problems. Please fix this otherwise, it would not be useful to use.

    Reply
    • mathmathmath says:
      October 5, 2019 at 4:25 pm

      I will look at it.

      Reply
  8. Glover says:
    September 5, 2019 at 4:14 pm

    find the sum of (cos(2/n^2)-cos(2/(n+1)^2)) from 1 to infinity

    Reply
    • mathmathmath says:
      September 5, 2019 at 4:25 pm

      cos(2) – 1

      Reply
  9. Cale says:
    September 7, 2019 at 4:17 pm

    Very helpful website! Can you help me on the following:
    sin(5n)/(1+sqrtn)
    I know it converges, but to what?

    Reply
    • mathmathmath says:
      September 7, 2019 at 4:27 pm

      What are the limits for n?

      Reply
  10. Louis A. says:
    September 9, 2019 at 4:17 pm

    Determine the number of terms, n, given the geometric series -2 – 6 – 18 – 54 – … and Sn=−2186

    Reply
    • mathmathmath says:
      September 9, 2019 at 4:27 pm

      The number of terms is 7.

      Reply
  11. Redding says:
    September 9, 2019 at 4:18 pm

    Why the sum of ((1/3)^x)*x to infinite is equal to 3/4.
    I know that the sum of geometric series (1/3)^x will converge to 3/2, with formula a/(1-(1/3)). But ((1/3)^x)*x is no longer geometric series. Therefore I don’t know the algothrim anymore. Can anyone show me how to get the answer?

    Reply
    • mathmathmath says:
      September 9, 2019 at 4:31 pm

      A geometric series is given by the sum of a*n^x as x goes from 1 to infinity. Its sum is a*n/(1-n)
      Differentiate both sides with respect to n: a*x*n^(x-1) as n goes from 1 to infinity equals a/(1-n)^2

      Since n^(x-1) = n^x / n, then a*x*n^(x-1) = (a/n) x n^x and this sum equals a/(1-n)^2

      Therefore, the sum of x n^x equals a/(1-n)^2 * (n/a) = n/(1-n)^2

      In your case n=1/3: the sum is (1/3)/(1-1/3)^2=3/4

      Reply
  12. Albert D. says:
    September 26, 2019 at 4:18 pm

    Great calculator! I was trying to find this sort all along to finish my homeworks

    Reply
    • mathmathmath says:
      September 27, 2019 at 4:27 pm

      Thank you for your words!

      Reply
  13. Cynthia says:
    October 1, 2019 at 4:16 pm

    can’t find the answer: sum from 1 to inf of (n!)/((n+1)!+n^(1/2))

    Reply
    • mathmathmath says:
      October 1, 2019 at 4:26 pm

      The series diverges.

      Reply
  14. aura S says:
    October 1, 2019 at 4:18 pm

    I have an infinite series that seems to have bested your website and was wondering whether it was solvable- I couldn’t find many series like it:
    .1n(.9^(n-1))
    The partial sum reaches its practical limit at 10 and the websites I check against agree that it converges, but I would like to know if there is a way to find the true limit. Thanks!

    Reply
    • mathmathmath says:
      October 1, 2019 at 4:33 pm

      What does the dot sign mean?

      Reply
      • aura S says:
        October 5, 2019 at 4:34 pm

        That was a decimal point- .1n=0.1n, .9=0.9

        Reply
        • mathmathmath says:
          October 5, 2019 at 4:35 pm

          The answer is 10. You want steps?

          A geometric series is given by the sum of a*x^n as n goes from 1 to infinity. Its sum is a*x/(1-x)
          Differentiate both sides: a*n*x^(n-1) as n goes from 1 to infinity equals a/(1-x)^2

          You have 0.1n(0.9^(n-1)), so in your case a=0.1, x=0.9: the sum is 0.1/(1-0.9)^2=10

          Reply

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