Question

Prove that : 3^1/2.3^1/4.3^1/8………..=3​

Answer 1

Step-by-step explanation:

we know that if r<1

a+ar+ar^2+.......= a/(1-r)

now,

3^1/2 + 3^1/4 + 3^1/8 +.........

= 3^{1/2+1/4+1/8+.....)

here in exponent,

a= first term = 1/2

r= common ratio =1/2 which is less than one.

hence, sum = a/(1-r)

= 1/2/(1-1/2)

= 1

hence, the problem becomes 3^1

which is 3..proved