Latest Maths Olympiad Aptitude Question SOLUTION: If n is less than 1000000 then find the sum of 2+4+8+16+32+64+128+........+n

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(#M40033154) MATHS OLYMPIAD Logical Reasoning question simplify Keep an EYE

If n is less than 1000000 then find the sum of
2+4+8+16+32+64+128+........+n

Asked In Maths Olympiad Harsh Poddar (10 years ago)

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Sajal Garg  (10 years ago)

Its clear that the given series is GP
so a=2 & r=2 & n=?
first find nth term,
according to condition , 1000000> a*r^(n-1) => 1000000>2*2^(n-1)
taking n= 20, we got 1000000> 1048576 which is not true
so n should be less than 20, lets take n=19 now, 1000000 > 524288
so n=19.
now simply find sum of GP series where a=r=2 & n=19
sum={2*(2^19-1)}/2-1
sum= 1048574....

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Palash   (10 years ago)

It is in G.P. series where r=2 like (2^1+2^2+...)
Let there r n term.
So , 2^n=10^6
=> n=19.93
we will take 19 .
So the summation is {2.(2^19-1)}/(2-1)=1048574

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