Sum of the infinite series ((-1)^n * (-7)^n)/n

[Erubus]

Homework Statement

Find the sum of infinite the series (-1)^n * 7^n/n! for n=1 to infinity

Homework Equations

e^x = sum (x^n)/n! for n=0 to infinity

The Attempt at a Solution

I combined the (-1)^n and the 7^n to make the summation ((-7)^n)/n! for n = 1 to infinity

then I changed the lower bound to 0 to make it similar to e^x

((-7)^(n+1))/(n+1)! for n=0 to infinity

I don't know where to go from here, help would be appreciated!

 

[tiny-tim]

Welcome to PF!

Hi Erubus! Welcome to PF!

(try using the "Quick symbols" box, and the X² button just above the Reply box )

I combined the (-1)ⁿ and the 7ⁿ to make the summation ((-7)ⁿ)/n! for n = 1 to infinity

then I changed the lower bound to 0 to make it similar to e^x

((-7)ⁿ⁺¹)/(n+1)! for n=0 to infinity

instead of changing the limits, just add a "0th" term …

-1 + ∑₀^∞ (-7)ⁿ/n!

 

[Erubus]

Wow never would have thought of that, but it makes sense.

Thanks!