michaelxavier
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In Rudin's Principles of Mathematical Analysis, 3rd ed., I encountered the following on p. 10, and I'm not really sure where it comes from. I'll write it just as it is shown in the book.
The identity
b^n-a^n=(b-a)(b^(n-1)*a^0 + b^(n-2)*a^1 + ... + b^1*a^(n-2) + b^0*a^(n-1))
yields the inequality
b^n-a^n<(b-a)n*b^(n-1)
when 0<a<b
I understand where the indentity comes from. I'm just confused about the inequality, and I was curious. Thanks for sharing any ideas.
The identity
b^n-a^n=(b-a)(b^(n-1)*a^0 + b^(n-2)*a^1 + ... + b^1*a^(n-2) + b^0*a^(n-1))
yields the inequality
b^n-a^n<(b-a)n*b^(n-1)
when 0<a<b
I understand where the indentity comes from. I'm just confused about the inequality, and I was curious. Thanks for sharing any ideas.