LCM of 6,12,20, and so on?
1 1 − 6 5 + 1 2 7 − 2 0 9 + 3 0 1 1 − 4 2 1 3 + 5 6 1 5 − 7 2 1 7 + 9 0 1 9
If the expression above is in the form of b a for coprime positive integers a , b , find a + b ?
The answer is 8.
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6 solutions
But this question isn't fully clear, because 3/5 can also be 6/10,18/30,etc. It should have been written that a/b should be in its simplest form.
Very nice .....
what about numarator values from second step
what about numarator values from second step...?
90 can be divided as 45 X 2 then why did u choose 9X10 nd ho w can we make sure that the way ehich we have split the denominator is going to be use
Write the sum out in sigma notation:
1 1 + n = 1 ∑ 8 ( − 1 ) n ( n + 1 ) ( n + 2 ) 2 n + 3 = 1 + n = 1 ∑ 8 ( − 1 ) n ( n + 1 1 + n + 2 1 )
This is a telescoping sum, and thus the only terms left are
1 − 2 1 + 1 0 1 = 5 3
Also, I'm curious: is Class 7th equivalent to Secondary 1 (ages 12-13)?
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Sorry , by mistake I wrote it here , I was going to post another problem given by him but that too easy one, Thanks for solving it
my grade 7 class had 11-13 the 11 year olds were November born and the 13 year olds were the previous year's December born. So your answer is yes.
would u mind telling how did u get that no.s from the summation series...I'm curious to know ,how to solve the sigma of powers.
1 - 5/6 +7/12 - 9/20 + -.......+19/90
= 1 - (2+3)/(2x3) + (3+4)/(3x4) - + .......+(9+10)/(9*10)
= 1 - 1/2 -1/3 +1/3 +1/4 -1/4 -1/5 +..............+1/9 +1/10
1/2, 1/3.........1/9 gets cancelled and finally, we get
1 - 1/2 +1/10 = 3/5 = a/b
a = 3, b = 5
a + b = 8
1/1=6/6 therefore 6/6-5/6=1/6, 1/6=2/12 therefore 2/12+7/12=9/12, 9/12=15/20 therefore 15/20-9/20=6/20, 6/20=9/30 therefore 9/30+11/30 = 20/30, 20/30=28/42 therefore 28/42-13/42=15/42, 15/42=20/56 therefore 20/56+15/56=35/56, 35/56=45/72 therefore 45/72-17/72=28/72, 28/72=35/90 therefore 35/90+19/90=54/90, 54/90=6/10=3/5 therefore 3+5= 8
guesses sometimes are really helpful??????