Question

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Answer 1

a/b=?

a=

$\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + ... + \frac{1}{42 \times 43}$

=>

$\frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ... + \frac{1}{42} - \frac{1}{43}$

se simplifică -1/2 cu 1/2,-1/3 cu 1/3...-1/42 cu 1/42

Si va ramane

$\frac{1}{1} - \frac{1}{43}$

amplificam prima fractie cu 43

$\frac{43 - 1}{43}$

$= \frac{42}{43}$

b.

b=

$\frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \frac{1}{4 \times 5} + ... + \frac{1}{125 \times 126}$

=>

$\frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + \frac{1}{4} - \frac{1}{5} + .... + \frac{1}{125} - \frac{1}{126}$

se simplifică -1/3 cu 1/3,-1/4 cu 1/4,-1/5 cu 1/5... -1/215 cu 1/215

Si va ramane

$\frac{1}{2} - \frac{1}{126}$

amplificam prima fractie cu 63

=>

$\frac{63 - 1}{126}$

$= \frac{62}{126}$

$\frac{a}{b} = ...$

$\frac{a}{b} = \frac{ \frac{42}{43} }{ \frac{62}{126} }$

$\frac{42}{43} \times \frac{126}{62 } = ...$

$\frac{5292}{2666}$