Maths Tricks for Comp. Exams
The sum of the first n natural numbers
n (n+1)/2
sum of
squares of n natural numbers
The sum of the cubes of the
first n natural numbers
The sum of the first n odd natural numbers
(2n-1) = n2
sum of first
n even numbers
n(n+1)
example:
The sum of first
n natural numbers = n (n+1)/2
Eg The sum of 1+2+3+……..+10+11+12 = ??
Here n = 12 so Sum = 12 ( 12+1 ) / 2
=
12 * 13 /2 = 6 * 13 = 78
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The sum of squares
of first n natural numbers is
n (n+1)(2n+1)/6
Eg the sum of 12 + 22 + 32 + 42
+ ………. +122 =??
=
12 (12+1) (2*12 + 1) /6
=
12*13*25 /6 = 650
The sum of first
n even numbers= n (n+1)
Eg The sum of 2+4+6+8+10+…………. +40 = ??
Here n ≠40.
N is the no of terms. So number of terms here is 20, the value of 20th term is 40 indeed.
So with n = 20
Sum
= 20 (20+1) =20*21 =420
The sum of first
n odd numbers= n2
Eg The sum of 1+3+5+7+9+11+…………..+21
Here n≠21. Here number of terms are 11 so n=11.
Sum
= 112 = 121
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Trick 1:
Q- If Rakesh paid 15% of his salray against
loan and spend 30% of his remaining salary in house hold expenses. if he
save Rs. 2380, what is his total income.
A- 100*100*2380
(100-15)(100-30)
= 4000
Trick- 100 * 100 * save money
( 100-first expense) (100-second expense)
A- 100*100*2380
(100-15)(100-30)
= 4000
Trick- 100 * 100 * save money
( 100-first expense) (100-second expense)
Trick 2:
Q- If in exam 45%
student fail in Maths, 30% student in English and 20% in both exam. What
percantge of students pass in both subject ?
Ans:- In this question 45% student fail in maths and 30% student fail in English and 20% student in both exam. It means total 20% of student fail in both Math and english. So what you have to do you just subtract 20% from both maths and english fail students. which comes like this.
45-20=25 (it means 25% student only fail in maths)
30-20=10 (it means 10% student only fail in english)
and total percentage of student fail in both exam are 20%
from this we now say like this
total percentage of student fail are 25+10+20=55%
Therefore, total student pass in both subject are 100-55=45% .
Trick- 100-(Maths fail + English fail - both subject fail student )
Ans:- In this question 45% student fail in maths and 30% student fail in English and 20% student in both exam. It means total 20% of student fail in both Math and english. So what you have to do you just subtract 20% from both maths and english fail students. which comes like this.
45-20=25 (it means 25% student only fail in maths)
30-20=10 (it means 10% student only fail in english)
and total percentage of student fail in both exam are 20%
from this we now say like this
total percentage of student fail are 25+10+20=55%
Therefore, total student pass in both subject are 100-55=45% .
Trick- 100-(Maths fail + English fail - both subject fail student )
have fun .......waiting for comment
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