1This one came in tensors??????
sum 1 tel me...................... Sum of d factors of 10! which are odd and are of d form "3m+2", m belongs to N
-
UP 0 DOWN 0 2 9
9 Answers
341The primes that divide 10! are 2,3,5 and 7 and we know how to compute the highest power of a prime that divides n!
Hence 10! = 2834527
Now you can check that
(3m+2)(3m+2) gives 3m+1
(3m+1)(3m+1) gives 3m+1
(3m+1)(3m+2) gives 3m+2
Now the problem requires us to ignore factors with powers of 2 and 3
5 is of the form 3m+2 while 7 is of the form 3m+1.
Hence 5 is one such factor, and the other is 35
5+35 = 40
341for the integral put x = f(t). So the limits become 0 to 2 and the integrand becomes t(et + 3/2 e-3t/2). This is easy to integrate by parts
24"Now you can check that
(3m+2)(3m+2) gives 3m+1
(3m+1)(3m+1) gives 3m+1
(3m+1)(3m+2) gives 3m+2
Now the problem requires us to ignore factors with powers of 2 and 3
5 is of the form 3m+2 while 7 is of the form 3m+1."
62(3m+2)(3m+2) gives 3m+1
(3m+1)(3m+1) gives 3m+1
(3m+1)(3m+2) gives 3m+2
this i thought is obvious!
i mean multiply them and you will be left with 3k+4, 3k+1 and 3k+2 respectively!
After this.. you dont want an even number.. so you will not take any power of two..
also the number is of the form 3n+2 .. so it is nto a multiple of 3... so you have to ignore any power of 3 too..