Problem with this challenging summation I'm having some trouble finding the summation of this series. I tried all I could, but in the end the denominator is creating problem. sum_(r=0)^(n) (-1)^r ((n),(r))(1+r ln 10)/((1+ ln 10^n)^r)

Angel Kline

Angel Kline

Answered question

2022-10-29

Problem with this challenging summation
I'm having some trouble finding the summation of this series.
I tried all I could, but in the end the denominator is creating problem.
r = 0 n ( 1 ) r ( n r ) 1 + r ln 10 ( 1 + ln 10 n ) r
The answer is zero but in my book no solution is given.
Any help would be appreciated.

Answer & Explanation

Warkallent8

Warkallent8

Beginner2022-10-30Added 16 answers

Hint:
r = 0 n ( n r ) x r = ( 1 + x ) n
r = 0 n r ( n r ) x r = x d d x r = 0 n ( n r ) x r = n x ( 1 + x ) n 1

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