Can someone please explain to me what this sigma notation means in this formula. Im confused because there is no top number on the sigma and what does this sum mean on the bottom?
and also this is the formula for the multinomial theorem, what are the $k_m$ values supposed to represent?
$$(x_1+x_2+…+x_m)^n=\sum_{k_1+k_2+…+k_m=n}{n \choose k_1,k_2,…,k_m}\prod_{t=1}^mx_t^{k_t}$$
Sigma notation confusion
algebra-precalculusnotation
Best Answer
$\sum_{k_1+k_2+...+k_m=n}$ means you're considering the sum over all elements of the following set $$\bigg\{(k_1,k_2,\ldots,k_m):\sum_{i=1}^mk_i=n,0\leq k_i\leq n\bigg\}$$