Question

Find an expression for the general term of the series below. Assume the starting value of the index, k, is 0.

Answer 1

\[(x-5)^4 - \frac{ (x-5)^7 }{ 2!} + \frac{ (x-5)^{10} }{ 4! } - \frac{ (x-5)^{13} }{ 6! }+ . . .\]

Answer 2

@satellite73 can you help me please

Answer 3

the odd terms always negative, while even terms positive... it means the terms has (-1)^(n+1), for n is natural number

Answer 4

the power of (x-5) is the aritmetic sequence with the terms 4,7,10,13,...

Answer 5

just use the formula :
an = a1 + (n-1)d
an = 4 + (n-1)3
an = 3n + 1

Answer 6

for the factorial's 0!, 2!, 4!, 6!, ... so on use the arithmetic sequence too