Grade 12th passAlgebra

the product (32) (32)^1/6 (32)^1/36.......infinity is equal to?????

mansi dabriwal

11 Years agoGrade 12th pass

4 Answers

Latika Leekha

Approved Tutor Answer11 Years ago

Hello student,
The given series is (32) (32)^1/6(32)^1/36 ….…...... infinity
= (32) ^{1+1/6+1/36 + …. ∞}
Now, 1+1/6+1/36 + …. ∞
= 1/1-1/6
= 6/5.
So, (32) (32)1/6(32)1/36 ….…...... ∞
= (32) ^{1+1/6+1/36 + …. ∞}
= (32)^6/5
= 2⁶
= 64.

mansi dabriwal

11 Years ago

thanx.....got it..:)

alex

10 Years ago

wait, how did u get 1/1-1/6 to be 6/5? and why 1/1-1/6 in the 1^st place?? how? plz tell me how?? it just doesnt make sense

Panda

9 Years ago

the formula of sum of infinite terms in a geometric progression is a/(1-r),where “a”is the first term.As 1+(1/6)+(1/36)+.......upto infinity is a geometric progression,we use that formula here.