# Thread: sum of first n terms

1. ## sum of first n terms

i got stucked at part a , how should i proceed form the previous steps? i know that the (2n-1)^2 -(2n)^2 +(2n+1)^2 = (1)^2 -(2)^2 +(3)^2

2. ## Re: sum of first n terms

so (2n+1)(-n+2n+1)
sum=(2n+1)(n+1)
of a part

3. ## Re: sum of first n terms

Originally Posted by prasum
so (2n+1)(-n+2n+1)
sum=(2n+1)(n+1)
of a part
can you explain why would you do so? i cant understand

4. ## Re: sum of first n terms

u know the sum of 1^2-2^2+3^2-4^2+...(2n-1)^2-(2n)^2=-n(2n+1)
u have extra term=(2n+1)^2
so just add these two to get ur final sum as:
-n(2n+1)+(2n+1)^2
so (2n+1)(-n+2n+1)
sum=(2n+1)(n+1)
of a part

5. ## Re: sum of first n terms

why is it not necessary to find the new sum again? but just to take the old sum and plus with the new terms?

6. ## Re: sum of first n terms

because u have already found out from the previous question
the sum 1^2-2^2+3^2-4^2+...(2n-1)^2-(2n)^2=-n(2n+1)
in these type of questions u use what u have proved above