Not so tough

Algebra Level 4

$\left(1 + \frac{1}{3}\right)\times \left(1 + \frac{1}{3^2}\right) \times \left(1 + \frac{1}{3^4}\right) \times \left(1 + \frac {1}{3^8}\right) \times \left(1 + \frac{1}{3^{16}}\right) \times \cdots = \ ? \$

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The answer is 1.5.

2 solutions

Neelesh Vij
Jan 26, 2016

Hint: Multiply numerator and denominator by $( 1 - \frac{1}{3} )$ and see the magic

but how the answer has become 1.5?

sakshi rathore - 5 years, 4 months ago

now use (a+b)(a-b)=a^2-b^2. see the first two terms will multiply to give 1^2-1/3^2 continuing this pattern u see that it becomes 1-1/3^infinity omg denominator is too large .so 1/3^infinity becomes zero now let the value of above question be x then 2/3x=1 x=3/2 if u dont understand ask where u dont understand And if u do ,Follow me for more!!!!!

Kaustubh Miglani - 5 years, 4 months ago

Kush Singhal
Feb 9, 2016

Another way to do this is to realize that every term in the expansion of this product will be of the form $\frac {1}{3^n}$ for all natural number n Then just use summation of infinite GP with common ratio $\frac {1}{3}$ and first term 1 Therefore answer is 1.5

Not so tough

The answer is 1.5.

2 solutions

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