Question

Find the calue of 1+2+3+4+5------------------------------+45

Answer 1

Sum of 1st n natural numbers = n(n+1)/2 N=45 45×46/2 45×23 =1035

Answer 2

1−2+3−4+5+...+43−44+451−2+3−4+5+...+43−44+45

=(1−2)+(3−4)+(5−6)+...+(43−44)+45=(1−2)+(3−4)+(5−6)+...+(43−44)+45

Here we group together every other term. These are pairs of numbers that sum to -1. There are 22 of these pairs altogether, plus the 45 at the end.

=(−1)+(−1)+(−1)+...+(−1)+45=(−1)+(−1)+(−1)+...+(−1)+45

=22(−1)+45=22(−1)+45

=23=23

Hope this helps!