maths

find the sum of the infinite series (2/9)^2-(2/9)^3+(2/9)^4-(2/9)^5+ ...

  1. 👍
  2. 👎
  3. 👁
  1. (2/9)^2-(2/9)^3+(2/9)^4-(2/9)^5+
    This is like a geometric series with the first terms missing
    1 -1(2/9)^1 +1(2/9)^2-1(2/9)^3+(2/9)^4-(2/9)^5+
    so if we find the sum of that series and subtract [1 -1(2/9)^1], we have it
    so
    g = 1
    r = -2/9
    in Sn = g (1-r^n)/(1-r)
    n is infinite and |r| < 1
    so Sn =g/(1-r)
    Sn = 1/(1-2/9) = 1.286
    so we want
    1.286 -[1-2/9]
    .508

    1. 👍
    2. 👎
  2. Whoa - typo
    Sn = 1/(1+2/9) because r = -2/9
    Sn = .818
    so we want
    .818 -[1-2/9]
    .040

    1. 👍
    2. 👎
  3. i need help

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. sum geometric series

    what is the sum of geometric infinite series 3/2+ 9/16+ 27/128+ 81/1024=.... i know the formula is S=a/(1-r) my teacher, he usually transforms into a formula of the sum series and finds out a and r.but i don't how to do that. the

  2. Algebra 2

    Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first four terms of the sequence? a{1} = first term of series ∞ Infinite Sum = ∑ a{1} • r^(n – 1) = a{1} ⁄ (1 – r)

  3. Math

    Calculate the sum of the infinite series 72 + 60 + 50 + 125/3 + ... 489 432 360 307 Can someone please help me with this one? I can never solve these on my own:(

  4. Math

    Does the following infinite geometric series diverge or converge? Explain. 3 + 9 + 27 + 81 + . . . A) It diverges; it does not have a sum. B) It converges; it has a sum.*** C) It diverges; it has a sum. D) It converges; it does

  1. Math

    Determine whether the infinite geometric series converges. If so, find the sum 1/4+1/16+1/64+1/256....

  2. Math

    Does the following infinite geometric series diverge or converge? Explain. 1/7+1/28+1/112+1/448 A) It converges; it has a sum.*** B) It diverges; it does not have a sum. C) It diverges; it has a sum. D) It converges; it does not

  3. Calculus

    Find the sum of the infinite series whose sequence of partial sums, Sn, is S sub n equals= 10-1/(n+1) a) 10 b) 0 c) 9.99 d) Sum does not exist

  4. Math

    Does the following infinite geometric series diverge or converge? Explain. 1/5 + 1/25 + 1/125 + 1/625 A) It diverges; it has a sum. B) It converges; it has a sum. C) It diverges; it does not have a sum. D) It converges; it does

  1. Calculus

    By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series. A) 1+5 + (5^2)/(2!)+(5^3)/(3!)+(5^4)/(4!)+...+ (5^k)/(k!)+...= B)

  2. math

    Consider two infinite geometric series. The first has leading term $a,$ common ratio $b,$ and sum $S.$ The second has a leading term $b,$ common ratio $a,$ and sum $1/S.$ Find the value of $a+b.$

  3. Math

    1.calculate the sum of the infinite series S(infinity)=16+4+1+..., (1 point) A. -16/3 B.64/3 C.12 D. It does not converge 2.Which of the following formulas can be used to write 0.797979... as a fraction?

  4. Math

    which of the following is true statement ? a. a finite series has no sum b. any finite series has a sum c. some infinite arithmetic series have a sum d. all infinite arithmetic series have a sum

You can view more similar questions or ask a new question.