Problem 47083. sum of binomial series

The k-th term of the series T(k,x,n) is given as:
T(k,x,n) =k* (x^(k-1))*((n!)/(k!*(n-k)!)).
where n! = 1*2*3......n
Find the sum S = sum(T(k,x,n)) for k = 1 to n.
Hint : try binomial expansion of (1+x)^n and its derivative, for a smarter solution.
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Solution Stats

81.25% Correct | 18.75% Incorrect
Last Solution submitted on Aug 11, 2025

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