SOLUTION: Hi im having so much trouble proving this formula with mathematical induction. Please help! {{{ 1/(1*3)+1/(3*5)}}}+...+{{{+1/((2n-1)(2n+1))=n/(2n+1) }}} Basis step: n=1 was

SOLUTION: Hi im having so much trouble proving this formula with mathematical induction. Please help! {{{ 1/(13)+1/(35)}}}+...+{{{+1/((2n-1)(2n+1))=n/(2n+1) }}} Basis step: n=1 was

Question 1021838: Hi im having so much trouble proving this formula with mathematical induction.
Please help!
+...+
Basis step: n=1 was true
Assumption step: n=k

Induction step: Prove true for n=(k+1)
+...++
+...++
From here I have no idea what to do, to the LHS to make it equal to RHS

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The assumption of induction is:
+...+
Now add to BOTH sides.
==> +...+
(Note: 1) The last equation is TRUE by the induction hypothesis. 2) We added 1/(2k+1)(2k+3) because it is supposed to be the next term in line after 1/(2k-1)(2k+1).)
The RHS of the last equation is equal to

=
= =

I leave the rest of the inductive argument to you...
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