prove that Sn=n(n+1) for the sequence an=2n,where n is any positive integers​

Question

prove that Sn=n(n+1) for the sequence an=2n,where n is any positive integers​

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Nho 3 years 2021-08-23T13:05:22+00:00 1 Answers 0 views 0

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  1. haidang
    0
    2021-08-23T13:06:23+00:00
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    Answer:

    Proved

    Step-by-step explanation:

    Given

    a_n = 2n

    Required

    Prove that S_n = n(n+1)

    The given sequence is an arithmetic sequence.

    The Sn of this sequence is:

    S_n = \frac{n}{2}(a_1 + a_n)

    Calculate a1

    a_n =2n

    a_1 =2*1

    a_1 =2

    So, we have:

    S_n = \frac{n}{2}(a_1 + a_n)

    S_n = \frac{n}{2}(2 + 2n)

    Factor out 2

    S_n = \frac{n*2}{2}(1 + n)

    S_n = n(1 + n)

    S_n = n(n + 1) — Proved

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