i messed up the forum index
Now by the principle of mathematical induction u can prove that X is either equal to or greater than Y.
we kno that last term of the AP = last term of the GP
then how did u get that
sum of AP = sum of GP..
Let the number of terms be n. Then the sum of terms of the AP is
Suppose the common ratio of the terms is r, then
Now the sum of terms of the GP can be written as
The typical bracketed term is
We will now prove that this is less than or equal to a+b =
WLOG we may assume that r>1 (otherwise we read the sequence backwards)
So we are to prove that
Hence, each bracketed term is less than or equal to a+b.
Hence the entire sum is less than or equal to thus proving the statement