Question

Find the sum of the series 2/9+1/3+1/2+........+81/32.

Answer 1

Answer:

a=2/9. , r= (-1/3×9/2)= -3/2. , Sn= 55/72. , n=?

Sn=a.(1-r^n)/(1-r)

55/72. = (2/9). [1-(-3/2)^n]/(1+3/2)

(55/72)×(9/2)×(5/2)=1-(-3/2)^n

275/32=1-(-3/2)^n

or. (-3/2)^n. = 1–275/32=(32–275)/32=(-243)/32 = (- 3)^5/(2)^5.

or. (-3/2)^n=(-3/2)^5

or. n = 5 terms.

Answer.