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

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The discussion centers on proving the formula Sn=(-1)^n(n+1) for the sequence Sn=1-3+5-7...+(-1)^n(2n+1) using mathematical induction. The user attempts to establish the proof by calculating S(n+1) and simplifying it, but fails to validate the base case for n=1, which is crucial for induction. The user also provides values for S2 and S3, indicating a misunderstanding of the proof's requirements. The conclusion emphasizes the necessity of confirming the base case to complete the induction proof.

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

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