Answer:
(-21)+(-20)+(-19)+...+50 is equal to 1044
Step-by-step 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.
