Induction Proof of Loop Invariance Given the Invariance

Question

Consider the following program segment

i=1
total = 1

while i<n
  i = i + 1
  total = total + i

Let p be the proposition "total = $\frac{{i}{(i+1)}}{2}$ " and $ i ≤ n $ Use mathematical induction to prove the that p is a loop invariant.

Having issues simplifying and solving the problem.

1. I claim that the loop invariant is $t=\frac{{i}{(i+1)}}{2}$

2. I start off with the Base Case of i=1 and t=1 which proves to be true $$1 = \frac{{1}{(1+1)}}{2}$$

3. Now I let t_B and i_B be the values at the end of the x^th iteration of the loop and t_A and i_A be the vales after (x+1)^th iteration of the loop

4. So my Induction Hypothesis is that my loop invariant holds at the end of the x^th iteration

$$IH: t_b = \frac{{i_b}{(i_b+1)}}{2}$$

Whereas

t_A = t_B + i_B

i_A = i_B + 1

And my guard condition is i_b ≤ n

So then we would have

$$ t_a = t_b+i_a $$ $$ = \frac {{i_b}{(i_b+1)}}{2} + ia $$ $$ = \frac {{i_b}{(i_a)}}{2} + \frac{2i_a}{2}$$ $$ = \frac {{i_b}{(i_a)}+{2i_a}}{2}$$ $$ = \frac {{i_a}{(i_b}{}+{i_a)}}{2}$$

And now I'm stuck. I'm having trouble understanding where to use the updated variables in the Induction proofs as one of the variables relies on its previous iteration. Thank you for your time everyone.

_{Update I've figured out subscripts}