I need help with finding the sum of $\sum \limits_{k=0}^{n} \frac{1}{k+1}{n\choose k}x^{k+1}$
2026-03-27 13:25:39.1774617939
Calculate sum with binomial coefficients: $\sum_{k=0}^{n} \frac{1}{k+1} \binom nk x^{k+1}$
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Hint
$$\sum \limits_{k=0}^{n} \frac{1}{k+1}{n\choose k}x^{k+1}=\int_0^x \sum \limits_{k=0}^{n} {n\choose k}t^{k}dt=\int_0^x(1+t)^ndt$$
Can you take it from here?