101+102+103..........200 ka maan kya hoga

Mathematics

ScanSolve AI Answer

Step-by-step solution

3 steps
  1. Identify the series.

    This is an arithmetic progression with the first term a1=101a_1 = 101, the last term an=200a_n = 200, and a common difference d=1d = 1.

  2. Find the number of terms (nn).

    The formula for the nn-th term of an arithmetic progression is an=a1+(n−1)da_n = a_1 + (n-1)d.
    Substitute the known values: 200=101+(n−1)×1200 = 101 + (n-1) \times 1.
    200−101=n−1200 - 101 = n - 1.
    99=n−199 = n - 1.
    n=99+1=100n = 99 + 1 = 100.
    There are 100 terms in the series.

  3. Calculate the sum of the arithmetic progression.

    The formula for the sum of an arithmetic progression is Sn=n2(a1+an)S_n = \frac{n}{2}(a_1 + a_n).
    Substitute the values: S100=1002(101+200)S_{100} = \frac{100}{2}(101 + 200).
    S100=50(301)S_{100} = 50(301).
    S100=15050S_{100} = 15050.

    101+102+103+⋯+200=15050101+102+103+\dots+200 = 15050

    The sum of the series is 15050.

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