Question

-21+-20+-19+.......+50

Answer 1

(-21)+(-20)+(-19)+...+50 is equal to 1044

Explanation:

Let's divide the number series and find its solution.

The original number series is:

(-21)+(-20)+(-19)+...+50 which is the same as:

{(-1)*(21+20+19+18+....+0)} + (1+2+3+...+50) which is

-A+B where:

A=(21+20+19+18+....+0)=(0+1+2+3+...+21)

B=(1+2+3+...+50)

For this problem, we can use the Gauss method, which establishes that for a continuos series of numbers starting in 1, we can find the sum by:

S=n*(n+1)/2 where n is the last value of the series, so:

Using the method for A we have:

S=n*(n+1)/2

S(A)=(21)*(21+1)/2

S(A)=231

Using the method for B we have:

S=n*(n+1)/2

S(B)=(50)*(50+1)/2

S(B)=1275

So finally,

-A+B=-231+1275=1044

In conclusion, (-21)+(-20)+(-19)+...+50 is equal to 1044.