tracyyahoo wrote:The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from n to m, inclusive, where 0<n<m?
A. m(m+1)/2 - (n+1)(n+2)/2
B. m(m+1)/2 - n(n+1)/2
C. m(m+1)/2 - (n-1)n/2
D. (m-1)m/2 - (n+1)(n+2)/2
E. (m-1)m/2 - n(n+1)/2
why c not b,pls explain in details
Let m=5 and n=3.
Sum of the integers 3 through 5 = 3+4+5 = 12. This is our target.
Now we plug m=5 and n=3 into the answers to see which yields our target of 12.
Answer choices A, B and C include m(m+1)/2:
m(m+1)/2 = 5(5+1)/2 = 15.
To yield our target of 12, we need to subtract 3.
Only answer choice C works:
(n-1)n/2 = (3-1)3/2 = 3.
Since m(m+1)/2 yields our target, the expression in D and E -- (m-1)m/2 -- will NOT yield our target.
The correct answer is
C.
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