C = 1^1 + 2^2 + 3^3 + ... + 999^999 + 1000^1000: identify 1st 3 digits from left

[King Math]

C = 1¹ + 2² + 3³ + ... + 999⁹⁹⁹ + 1000¹⁰⁰⁰
Please identify the first three digits from the left of the C.

 

[stapel]

C = 1¹ + 2² + 3³ + ... + 999⁹⁹⁹ + 1000¹⁰⁰⁰
Please identify the first three digits from the left of the C.

Please reply with a clear listing of your thoughts and efforts so far, starting with the formula(s), etc, that they gave you in class. Thank you!

 

[Deleted member 4993]

C = 1¹ + 2² + 3³ + ... + 999⁹⁹⁹ + 1000¹⁰⁰⁰
Please identify the first three digits from the left of the C.

999⁹⁹⁹ < 1000⁹⁹⁹

So

999⁹⁹⁹ + 1000¹⁰⁰⁰ < 1001 * 1000⁹⁹⁹ ..... and continue....