Evaluate
1/(1 + 2^0.5) + 1/(2^0.5 + 3^0.5) + ... + 1/(8^0.5 + 9^0.5) + 1/(9^0.5 + 10^0.5)
Dont know how to enter the square root sign so used ^0.5 instead.
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Evaluate
1/(1 + 2^0.5) + 1/(2^0.5 + 3^0.5) + ... + 1/(8^0.5 + 9^0.5) + 1/(9^0.5 + 10^0.5)
Dont know how to enter the square root sign so used ^0.5 instead.
These problems are always solved in the same way.
For each individual term:
1/(sqrt(a) + sqrt(b))
multiply by 1, where:
1 = (sqrt(a) - sqrt(b))/(sqrt(a) - sqrt(b))
That gets rid of the sqrts in the denominator and leaves you with integers, thus making it easier to deal with.
zaza
thanks for that method. It helped a lot. Made it so much easier.
2^0.5 - 1 + 3^0.5 - 2^0.5 + 4^0.5 - 3^0.5 ... = 10^0.5 - 1