Mathematical induction?

Question: Let Sn= 1/1x3 + 1/3x5 +1/5x7 + ....... + 1/(2n-1)(2n+1) for integers n≥1. Prove by induction that Sn=(1/2)(1-1/(2n+1) ) I am a little confused about induction. I have done the first step as shown below. Step 1: Prove true for n=1 LHS=1/(2(1)-1)(1(1)+1)=1/3... show more Question:

Let Sn= 1/1x3 + 1/3x5 +1/5x7 + ....... + 1/(2n-1)(2n+1) for integers n≥1.

Prove by induction that Sn=(1/2)(1-1/(2n+1) )

I am a little confused about induction. I have done the first step as shown below.

Step 1: Prove true for n=1

LHS=1/(2(1)-1)(1(1)+1)=1/3

RHS=1/2(1-1/2(1)+1)=1/2(1-1/3)= 1/2 x 2/3= 1/3

LHS=RHS. Therefore, n=1 is true.

Can someone please explain to me the rest of the proof in steps? Any help will be greatly appreciated. Thank you :)
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