Integration
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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.
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This solution is comprised of a detailed explanation to explain how to solve the attached problems (as much explanation as possible) and solve to the specified answers.
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Hi, herewith I have attached a file, which includes the answers, please go through it.
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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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