_______________________n
Consider the summation SUM ( (1/i) - (1/(i+1)) )
____________________ i=1
Derive a formula for this sum in terms of n.
n
Hint: SUM ( A(i) - A(i+1) )
i=1
= (A(1)-A(2)) + (A(2)-A(3)) + ... + (A(n)-A(n+1)) (who cancels??)
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_______________________n
Consider the summation SUM ( (1/i) - (1/(i+1)) )
____________________ i=1
Derive a formula for this sum in terms of n.
n
Hint: SUM ( A(i) - A(i+1) )
i=1
= (A(1)-A(2)) + (A(2)-A(3)) + ... + (A(n)-A(n+1)) (who cancels??)
Write out the first few terms:Quote:
Originally Posted by kashifzaidi
.
Now simplify. What do you notice? What conclusion do you draw?
Attachment 13692
I done the following according to my notes. My book says find the common thing and divide it by 2 on both sides. I cannot find any common. I dont know how do it futher..
Plz help me
This is a page from my book.
Attachment 13693
The answer is simply
These are known as collapsing sums.
Here only the first and last terms remain after subtraction.
