Proving Sn=(-1)^n(n+1) for Induction | Homework Solution

[mtayab1994]

Homework Statement

Sn=1-3+5-7...+(-1)^n(2n+1)

Homework Equations

Show that Sn=(-1)^n(n+1)

The Attempt at a Solution

S(n+1)=Sn+(-1)^(n+1)*(2n+3) = (-1)^n*(n+1)+ (-1)^(n+1)*(2n+3)
S(n+1)= (-1)^(n+1)*[(2n+3)-(n+1)] (because (-1)^(n+1)= - (-1)^n )
S(n+1)=(-1)^(n+1)*(n+2)

is that correct proof

 

[HallsofIvy]

Well, you haven't shown that it is true for n= 1, so, no. But that is easily fixed.

 

[mtayab1994]

Well, you haven't shown that it is true for n= 1, so, no. But that is easily fixed.

i did that before doing the work and for n=1 it came out to equal -3 and i also had to count S2 and S3 and i got 5 for S2 and -7 for S3.

But my proof is fine right?