Consecutive integers

[420024]

[Deleted because poster did not cite author.]

[th3414]

(100 + 150)/2=125 Mult 125*51(sum of #of terms +1)=6375

125-150/2=137.5, then 137.5*26=3575

6375-3575=2800

100+124/2=112, then 112*25=2800

I am just learning this too but i hope it helps!

[Guest]

[Deleted because poster did not cite author.]

The sum of the consecutive integers from 100 to 150 can be written as

(100)+(100+1)+(100+2)....(100+50)


The sum of the consecutive integers from 125 to 150 can be written as

(125)+(125+1)+(125+2)...(125+5)


We know that the 125 is the same as (100+25) so when you subtract the terms you will cross out everything after this entry to see whats left.


(100+25)+(100+26)......(100+50) Subtract (125)+(125+1)....(125+25)


All that you will have left over is:

(100)+(100+1)+(100+2)....(100+24) because we crossed out everything equal to 125 and everything after it.


Therefore it is equal to the sum of the consecutive integers from 100 to 124.

[StaceyKoprince]

please cite the author of the problem; otherwise it will be deleted. Thanks!