Question

Evaluate..
IF YOU CAN! MATHS SIMPLE
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Answer 1

Answer:

-19/20

Step-by-step explanation:

Each term can be changed as follows:

• 1/(1√2+2√1)=(2√1-1√2)/(4-2)= 1-√2/2

• 1/(2√3+3√2)=(3√2-2√3)/(2√3+3√2)(3√2-2√3)=(3√2-2√3)/(18-12)=√2/2-√3/3

...

• 1/(399√400+400√399)=...= √399/399-√400/400

Added up all terms get cancelled apart from the very first and very last:

• 1- √400/400= 1- 20/400= 1- 1/20= -19/20

Answer 2

Answer:

-19/20

Step-by-step explanation:

Each term can be changed as follows:

1/(1√2+2√1)=(2√1-1√2)/(4-2)= 1-√2/2

1/(2√3+3√2)=(3√2-2√3)/(2√3+3√2)(3√2-2√3)=(3√2-2√3)/(18-12)=√2/2-√3/3

...

1/(399√400+400√399)=...= √399/399-√400/400

Added up all terms get cancelled apart from the very first and very last:

1- √400/400= 1- 20/400= 1- 1/20= -19/20

Step-by-step explanation:

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