Question 1131967
<br>
The other tutor appears to have overlooked part of the statement of the problem.<br>
The two sums are the same, because each term of one sequence is the same as the corresponding term of the other sequence.<br>
First terms:
first sequence: 7(3/4)^2 = 7(9/16) = 63/16
second sequence: (63/16)(3/4)^0 = 63/16
Second terms:
first sequence: 7(3/4)^3 = 7(27/64) = 189/64
second sequence: (63/16)(3/4)^1 = 189/64
etc., etc.<br>
Formally....<br><pre>

   1000 
  (sigma) 7(3/4)^n  =
   n=2

      1000
   7*(sigma) (3/4)^n  =    [move the constant 7 outside the summation symbol]
      n=2

               1000
   (7(3/4)^2)*(sigma) (3/4)^(n-2)  =    [move 2 powers of (3/4) outside the summation symbol]
               n=2

            998
   (63/16)*(sigma) (3/4)^n    [redefine the index]
            n=0<br></pre>