nasty question - summing series

ra^r - (r-1)a^r-1 = (a-1)ra^r-1 +a^r-1

use this result to find ∑ ra^r-1 (to n terms)

im fairly sure it involves summing by differences but it doesnt seem to work out. :frown:

Reply 1

Neapolitan

Undry1

ra^r - (r-1)a^r-1 = (a-1)ra^r-1 +a^r-1

use this result to find ∑ ra^r-1 (to n terms)

im fairly sure it involves summing by differences but it doesnt seem to work out. :frown:

Consider summing the LHS and the RHS.

Summing the RHS involves a multiple of the sum you're looking for, and summing a geometric progression.

Summing the LHS can be done by the method of differences