Question

Find the sum of 7 terms of the series `16/27 - 8/9 + 4/3 -` ....

Answer 1

a = `16/27`

r = `(-3)/2`

S₇ = `16/27((((-3)/2)^7 - 1)/((-3)/2 - 1))`

= `16/27 xx ((-2187)/128 - 1)/((-5)/2)`

= `16/27 xx 2/(-5) xx (-2187 - 128)/128`

= `(-2315)/(27 xx 5 xx 4)`

= `463/(27 xx 4)`

= `463/108`