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 Apr15 comment How to calculate sum of combinations with different n and k @Sab The identities used are ${n \choose m}={n \choose n-m}$ and ${n \choose m}={n-1 \choose m-1}+{n-1 \choose m}$. You may see here. From the former the answer can be written as ${n+D \choose D}-1$. Apr12 comment What's the difference between $\sum_{r=1}^n(ar+b)$ and $\sum_{r=1}^nar+b$ The latter is correct. You can regard $u_r$ as $f(r)$. Apr10 revised How to calculate sum of combinations with different n and k added 16 characters in body Apr10 revised How to calculate sum of combinations with different n and k added 37 characters in body Apr10 revised How to calculate sum of combinations with different n and k added 109 characters in body Apr10 comment How to calculate sum of combinations with different n and k @Sab It's because ${n \choose m}={n \choose n-m}$. Apr10 answered How to calculate sum of combinations with different n and k Apr9 awarded Teacher Apr9 answered Number of the term Apr6 accepted What is the volume of $A'EF-ABD$? Apr5 asked What is the volume of $A'EF-ABD$? Mar9 accepted Show that $x^2+15y^2=4^n$ has at least $n$ non-negative integer solutions Mar8 revised Show that $x^2+15y^2=4^n$ has at least $n$ non-negative integer solutions added 73 characters in body Mar8 comment Show that $x^2+15y^2=4^n$ has at least $n$ non-negative integer solutions But, for $4^3$ I need $3$ solutions. Mar8 comment Show that $x^2+15y^2=4^n$ has at least $n$ non-negative integer solutions Sorry, I don't understand. It seems that this method can only generate even solutions? I have tried induction and $(x_{k+1}, y_{k+1}) = (2x_k, 2y_k)$. Mar8 asked Show that $x^2+15y^2=4^n$ has at least $n$ non-negative integer solutions Jan30 accepted Show that $\lim_{n \to \infty }(nx^{n+1}-(n+1)x^n)=0$ Jan29 asked Show that $\lim_{n \to \infty }(nx^{n+1}-(n+1)x^n)=0$ Jan20 awarded Supporter Jan20 awarded Informed