Question

1). an=3n²+2

2). an=2n³-1

3). an=n²+4

, Pahelp nman po.

Answer 1

Answer:

S = (n/2) ( 2n² + 3n + 5)

Step-by-step explanation:

an=3n²+2

a₁ = 3 * 1² + 2

a₂ = 3* 2² + 2

a₃ = 3* 3² + 2

Sum =a₁  + a₂ + a₃ + ...........................+ an  

S = 3 * 1² + 2  +  3* 2² + 2  + 3* 3² + 2  +..........................+ 3n²+2

=>S = 3 ( 1² + 2² + 3²  +...........+ n²)  + 2n

=>S = 3 n(n+1)(2n+1) /6  + 2n

=> S = n(n+1)(2n+1) /2  + 2n

=>S = (1/2) (n(n+1)(2n+1) +4n)

=> S = (n/2) ( 2n² + 3n + 1 + 4)

=> S = (n/2) ( 2n² + 3n + 5)