algorithm - Proof of Master theorem for Case-1: How these steps are mathematically derived? -

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i reading thomas h. cormen book understand proof of master theorem.however, stuck @ proving case-1.please me understand mathematical proofs more easy mathematical derivation of steps in following image:

enter image description here

thanks

for first question:

b^{\log_b(a)} =

(don't have tex in so?)

this because logarithm base b inverse of b^. a / = 1, b^epsilon remains.

second , third question: geometric series, can find here: https://en.wikipedia.org/wiki/geometric_series#formula
summand b^epsilon must between 0 , 1 (exclusive), i.e. |b^epsilon| < 1.


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