Short Quiz
1. Find 
2. Simplify 
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Categories: Problems
Quiz, Telescopic sum
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Hint: Try the assumption method in No. 1.
any clue for question no.2?
No. 2 is simply another stereotypical telescopic sum question. However, before doing the summation, some knowledge on surds (search Wikipedia) is required.
k i think i know how to do d
sorry i don know how to type the square root symbol
1 /1-/2
—– = —–
/1-/2 1-2
then,
1 1 /1-/2+/2-/3
—– + —– = ———– = /1-/3
/1-/2 /2-/3 (1-2)(2-3)
therefore when continue it to 1/(/2008-/2009), it will become
(/1-/2)+(/2-/3)+(/3-/4)+…+(/2008-/2009) /1 – /2009
—————————————– = ———- = /1 – /2009
(1-2)(2-3)(3-4)……(2008-2009) (-1)^2008
wah damn ugly..wait i organize again
1 /1-/2
——– = ——–—–
/1-/2 1-2
then,
1 1 /1-/2+/2-/3
———– + ———-– = ———–—– = /1-/3
/1-/2 /2-/3 (1-2)(2-3)
therefore when continue it to 1/(/2008-/2009), it will become
(/1-/2)+(/2-/3)+(/3-/4)+…+(/2008-/2009) /1 – /2009
——————————————————————-———– = ———- = /1 – /2009
(1-2)(2-3)(3-4)……(2008-2009) (-1)^2008
ok seriously damn ugly…
just tell the answer enough
square root of 1 – square root of 2009
The answer is supposed to be
, which is a negated answer of yours. Notice that
oh ya..i did wrongly
my answer should be (1-/2009)/-1 , which is /2009-1
k thanks