3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7
=3^2+ 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7
=3^2+2*3(3+3^2+3^3+3^4+3^5+3^6)
###(3+3^2+3^3+3^4+3^5+3^6) = ((3^6)-1)/(3-1) = 3*(((3^6)-1)/2)###
=3^2+2*3*3*((3^6)-1)/2 =3^2+3^8-3^2=3^8
Ans: "B"
The idea is to change the above series as a geometric series or part Geometric series;
3,3^2,3^3,3^4,3^5,3^6 are in geometric progression(G.P.).
a=first element of the series=3
r=ratio between two neighboring terms=3^2/3=3
n=number of elements=6
Sum of the G.P. = \(a(r^n-1)/(r-1)\) if r>1.
Since r=2>1
Sum of the G.P. of the above series= \(3(3^6-1)/(3-1)\)
_________________