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Algebra Level 5

Find the number of digits of the product below ( 1 + 2 ) ( 1 + 2 2 ) ( 1 + 2 4 ) ( 1 + 2 8 ) ( 1 + 2 16 ) ( 1 + 2 32 ) ( 1 + 2 64 ) ( 1 + 2 128 ) (1+2)(1+2^2)(1+2^4)(1+2^8)(1+2^{16})(1+2^{32})(1+2^{64})(1+2^{128})


The answer is 78.

Atul Shivam by Atul Shivam , 23, India

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1 solution

Aditya Kumar
May 6, 2016

Hint: write the (2+1) term as (2^2-1) , then keep applying a^2-b^2 identity and finally use the logarithm function to find the number of digits

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