calculus 2 changing lower bound power series

[paper heron]

Hello. I just wanted to ask because I wasn’t sure about this. I wanted to know why n changed from n=0 to n=1.

[rancid silo]

cause they changed n+1 to n

if you dont see it right away, do the sub k=n+1

you get the bottom line but k instead of n

[paper heron]

I know you’re suppose to plug in n+1 when changing the lower bound but how do I know what n equals to when I do that

[vivid hawk]

If you have a sum in terms of n

N= 0,1,2

If I replace every time n appears in the sum with n-1

I will be essentially doing n-1= -1,0,1….

So you remove the first one from the sum

[rancid silo]

n=k-1

$\sum_{n=0}^\infty\frac{(-1)^n}{n+1}\frac{x^{n+6}}{n+6}=\sum_{k=0+1}^\infty\frac{(-1)^{k-1}}{k}\frac{x^{k-1+6}}{k-1+6}$

[stone berry]

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