help needed with following question sigma notation question, thanks (1 Viewer)

[shmitler]

 

[Drongoski]

You can evaluate this as the sum of the sum of the 1st 20 terms of:
a GP: 3 + 9 + 27 + . . . and of
an AP: 1 + 3 + 5 + . . .

 

[jazz519]

Split it into two separate sums.

So sum of n=1 to 20 for (3^n) + sum of n=1 to 20 for (2n-1)

Then apply the geometric sum formula for the sum of n=1 to 20 for (3^n)
i.e. 3 + 9 + 27 + .... + = a(r^n-1)/(r-1) = 3*(3^20-1)/(3-1)

Then apply arithmetic series formula for sum of n=1 to 20 for (2n-1)
i.e. 1 + 3 + 5 +....+ 39 = n/2(a+L) = 20/2(1+39)

Then add them together

 

[shmitler]

thanks a lot