Question

The sum of all integers from -100 to 101 is

Answer 1

so sum of all integers from -100 to 101 is
let us arrange the numbers in series which are in ap
-100+(-99)+...............................+101
we know an=a+(n-1)d
here an=101
a=-100
d= a2-a1→1
n=n
substitute the values
101=-100+(n-1)1
201=n-1
n=202
we know Sn = [2a+(n-1)d]
Sn=n/2[2*-100+(202-1)1]
Sn=202/2[-200+201]
Sn =101
(OR)
there is an another method
the sum of all integers from -100to 101 is
-100+-99+................+99+100+101
so all negative will be cancelled out so answer is 101
I HOPE THIS WILL HELP U

Answer 2

Hey there!

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For this method we can use the formulas of A.P (Arthmetic Progression) Which comes at higher levels and formulas make this easy sum complicated


So let's go my second method which is easier and can be used in competitive exams for time saving :-

Q. To find Sum of all integers from -100 to +101

Ans. We have to find :

-100 + -99 + -98 ...... + 98 + 99 + 100 + 101

Here, We can clearly see all negative integers cancelled out each other... and remaining are : 0 and +101

=> 0 + 101
=> 101

Therefore, Sum of all integers is 101.


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Thanks!

Hope This Helps!

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