Question

∑（k=n,∞)(1-p)^(k-1)=(1-p)^(n-1)∑(k=0,∞)(1-p)^k

哪位大侠知道这个左边是怎么等于右边的呢？ 左边的式子怎么化成右边的

Answer 1

m=k-n, k = n+m, k=n->∞,m=0->∞.

∑（k=n,∞)(1-p)^(k-1)=∑（m=0,∞)(1-p)^(n+m-1)
=(1-p)^n∑（m=0,∞)(1-p)^(m-1)
=(1-p)^n∑（k=0,∞)(1-p)^(k-1)