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For each integer n>1, if S(n) denote the sum of even integer [#permalink]
25 Aug 2018, 12:40
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For each integer \(n>1\), if S(n) denote the sum of even integer upto \(n\) (not inclusive of \(n\)). For example, \(S(10)= 2+4+6+8=20\). What is value of \(S(300)\)? (A) \(22050\) (B) \(22350\) (C) \(22650\) (D) \(45150\) (E) \(90300\)
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Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
31 Aug 2018, 03:28
hi
can anyone tell whats the shortcut to such questions?



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Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
31 Aug 2018, 04:28
IshanGre wrote: hi
can anyone tell whats the shortcut to such questions? You need to be well versed with arithmetic progression formulas. It is not super complex just needs practice
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Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
31 Aug 2018, 05:40
IshanGre wrote: hi
can anyone tell whats the shortcut to such questions? First, you need to memorize the formula for the sum of arithmetic progression. Second, you need to know how to count number of terms. Third, practice and practice.



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Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
31 Aug 2018, 21:45
please tell the shortcut method to solve this question.



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Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
10 Nov 2018, 07:39
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S(300) = 2+..........+298
for number of terms, l = a+(n1)*2 298 = a+(n1)*2 = 2+(n1)*2 => 296/2 = n1 => n=149
for sum,
S(300) = n/2 * (a+l) = (149/2)*(298+2) = 149*150 = 22350
Answer is B!
Last edited by indiragre18 on 11 Nov 2018, 00:16, edited 1 time in total.



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Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
10 Nov 2018, 23:28
sandy wrote: For each integer \(n>1\), if S(n) denote the sum of even integer upto \(n\) (not inclusive of \(n\)). For example, \(S(10)= 2+4+6+8=20\). What is value of \(S(300)\)?
(A) \(22050\) (B) \(22350\) (C) \(22650\) (D) \(45150\) (E) \(90300\) there are three ways to do it .... (I) If you know that Sum of first n integers is \(\frac{n(n+1)}{2}\) Sum = \(2+4+6+...+300) = 2(1+2+3....+150)= 2 *\frac{150*151}{2}=150*151=22650\) (II) If you know that Sum of first n integers is \(\frac{n(n+1)[}{fraction]\) Now we have \([fraction]300/2}=150\) terms till 300, inclusive. Sum = \(2+4+6+...+300 = 150*151=150*151=22650\) (III) since it is an AP. the sum will be equal to Number of integers* average so \(150 * \frac{(300+2)}{2} = 150*151 = 22650\) Now subtract 300 from each result as the answered has to be exclusive of 300, that is 300 is not be included in total.. Therefore answer is 22650300=22350 B To know more about Arithmetic progressions https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048
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Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html



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Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
26 Nov 2018, 14:19
chetan2u wrote: sandy wrote: For each integer \(n>1\), if S(n) denote the sum of even integer upto \(n\) (not inclusive of \(n\)). For example, \(S(10)= 2+4+6+8=20\). What is value of \(S(300)\)?
(A) \(22050\) (B) \(22350\) (C) \(22650\) (D) \(45150\) (E) \(90300\) there are three ways to do it .... (I) If you know that Sum of first n integers is \(\frac{n(n+1)}{2}\) Sum = \(2+4+6+...+300) = 2(1+2+3....+150)= 2 *\frac{150*151}{2}=150*151=22650\) (II) If you know that Sum of first n integers is \(\frac{n(n+1)[}{fraction]\) Now we have \([fraction]300/2}=150\) terms till 300, inclusive. Sum = \(2+4+6+...+300 = 150*151=150*151=22650\) (III) since it is an AP. the sum will be equal to Number of integers* average so \(150 * \frac{(300+2)}{2} = 150*151 = 22650\) C To know more about Arithmetic progressions https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048According to the initial problem, the answer is B. Also it seems you are doing inclusive of n=300, while the prompt states NONinclusive.



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Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
26 Nov 2018, 18:05
projectoffset wrote: chetan2u wrote: sandy wrote: For each integer \(n>1\), if S(n) denote the sum of even integer upto \(n\) (not inclusive of \(n\)). For example, \(S(10)= 2+4+6+8=20\). What is value of \(S(300)\)?
(A) \(22050\) (B) \(22350\) (C) \(22650\) (D) \(45150\) (E) \(90300\) there are three ways to do it .... (I) If you know that Sum of first n integers is \(\frac{n(n+1)}{2}\) Sum = \(2+4+6+...+300) = 2(1+2+3....+150)= 2 *\frac{150*151}{2}=150*151=22650\) (II) If you know that Sum of first n integers is \(\frac{n(n+1)[}{fraction]\) Now we have \([fraction]300/2}=150\) terms till 300, inclusive. Sum = \(2+4+6+...+300 = 150*151=150*151=22650\) (III) since it is an AP. the sum will be equal to Number of integers* average so \(150 * \frac{(300+2)}{2} = 150*151 = 22650\) C To know more about Arithmetic progressions https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048According to the initial problem, the answer is B. Also it seems you are doing inclusive of n=300, while the prompt states NONinclusive. Yes, thank you. I had included 300 in each case. B will be the correct answer.
_________________
Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html




Re: For each integer n>1, if S(n) denote the sum of even integer
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