A whole life insurance policy is sold to the family of a newborn child. The policy pays 1000 if death occurs in the first year, 2000 in the second year, and so on up to 10,000 in the tenth year. The policy continues to provide coverage of 10,000 up to age 51. At age 51 and over it provides 50,000. Write the net single premium for this policy in terms of commutation functions.