_______________________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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Originally Posted by kashifzaidi _______________________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: . Now simplify. What do you notice? What conclusion do you draw?
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.
The answer is simply These are known as collapsing sums. Here only the first and last terms remain after subtraction.
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