Write the general formula for following alternating series in the form ?

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  • 2 months ago

    The nth term is 3/(n + 1)

    However, the terms alternate between positive and negative values.

    odd numbered terms are positive and even are negative

    i.e. (-1)ⁿ⁺¹...so, even values of n makes n + 1 odd

    => -1 raised to an odd power = -1

    so, 3(-1)ⁿ⁺¹/(n + 1)

    Checking with n = 4 gives:

    3(-1)⁵/5 => -3/5

    Hence, ∑ 3(-1)ⁿ⁺¹/(n + 1) => 3∑(-1)ⁿ⁺¹/(n + 1)

    :)>

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