A friend who owns a perpetuity that promises to pay $1,000 at the end of each year, forever, comes to you and offers to sell you all of the payments to be received after the 25th year for a price of $1,000.

In order to value perpetuity, received dividend must be divided by discount rate as;

= 1000/10% = $10,000, the dividend will value $10,000 today.

At an interest rate of 10%, should you pay the $1,000 today to receive payment numbers 26 and onwards? 

Actually No, because in this case perpetuity being worth $10,000 today, assuming discount rate remain unchanged in the 25th year. Now discounting back the investment, then;

= 10000(1.10)25 = $922.26; investment worth this amount today after discounting back all infinite payments of $1,000 starting in 26th year.

So, I think it has no sense to pay $1,000 for an investment that worth only $922.96 at the given 10% discount rate.

What does this suggest to you about the value of perpetual payments? 

The value of perpetuity payments will be constant at $10,000 assuming discount rate being constant but investor must also consider present value of investment through comparing price in dollars today with the intrinsic value of investment.