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    Please explain how to solve the attached problems (as much explanation as possible) and solve to the specified answers.

    Find a formula for the sum of n terms. Use the formula to find the limit as n approaches infinity.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:44 pm ad1c9bdddf
    https://brainmass.com/math/integrals/integration-sum-terms-59768

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    1. Find

    First we need find

    Then we have to apply the limit.

    Summation of I=1 to n = 16 [ 1/n^2+ 2/n^2+......n/n^2]

    = 16/n^2 [ 1+2+3+..........+n]

    = 16/ n^2 [Sn] -------------- ------ A

    Let us take Sn = 1+2+3+........n

    We know that Sn, 1+2+3+.......+n = {n(n+1)}/2

    We can prove this by mathematical induction method.

    LHS = 1+2+.....+n
    RHS = {n(n+1)}/2

    Put n = 1

    LHS =1 and RHS = {1(1+1)}/2 => 2/2 =1

    Therefore, LHS = RHS

    S(1) is true.

    Hence, S(k) is true.

    (ie) 1+2+3+.....+k = {k(k+1)}/2

    We shall now ...

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