Question

Find the sum to n terms of the series whose nth term is
n^2 - 2n + 2 + 2^n​

Answer 1

Step-by-step explanation:

$tn = {n}^{2} - 2n + 2 + {2}^{n}$

Sn = n/2[a+tn]

$t1 = {1}^{2} - 2 \times 1 + 2 + {2}^{1}$

$t1 = 1 - 2 + 2 + 2$

$t1 = 3$

$t2 = {2}^{2} - 2 \times 2 + 2 + {2}^{2}$

$t2 = 4 - 4 + 2 + 4$

$t2 = 6$

d = t2-t1 = 6-3 = 3

$sn = \frac{n}{2} 2a + {n - 1}d$

$sn = \frac{n}{2} 2 \times 3 + n - 1 \times 3$

$sn = \frac{n}{2 } \times 6 + 3n - 3$

$sn = \frac{n}{3} + 3n - 3$