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The sum to infinity of the series -5,-25,-125,625_____can be written as?
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The sum to infinity of the series -5,-25,-125,625_____can be written a...
Solution:
To find the sum to infinity of the given series, we need to first check if the series is a geometric progression or not.

  • Geometric Progression: A sequence of numbers is said to be a geometric progression if there is a common ratio between any two consecutive terms.

  • Let's check if the given series is a geometric progression or not:

  • Common Ratio = Next Term/Current Term

  • -25/-5 = 5

  • -125/-25 = 5

  • 625/-125 = -5

  • Since the common ratio is the same (-5 or 5) for all consecutive terms, the given series is a geometric progression.

  • Formula for the sum to infinity of a geometric progression: S∞ = a/(1-r)

  • Where, a = first term of the series and r = common ratio

  • For the given series, a = -5 and r = -5 (or 5)

  • Substituting the values in the formula, we get:

  • S∞ = -5/(1-(-5)) or S∞ = -5/(1+5)

  • S∞ = -5/6


Therefore, the sum to infinity of the given series is -5/6.
Community Answer
The sum to infinity of the series -5,-25,-125,625_____can be written a...
3125
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The sum to infinity of the series -5,-25,-125,625_____can be written as?
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