3) If and first term is ,
find the sum of the first 10 terms of the GP.
We have: .
Verify . . . True.4) Use mathematical induction to prove that: .
Add to both sides: .
And we have: .
We have proved . . . The proof is complete.
We have: .5) Expand: .
. . .
. . . .
. . .
For (1) you have used r= 10 in the denominator when r= -1.
(And, by the way, if it were 10, 1- 10= -9, not -11!)
For (2) you are fine until you get to and there you stop. Don't forget what you are trying to prove. You want to prove that sum is n(n+1) which, for n= k+1, is (k+1)(k+2). Factor !
For (3), has mysteriously become !