Without adding,find the sum: `1+3+5+7+9`

Find the sum: 5/3+ (3/5)

Find the sum: -2(1)/3+4 (3/5)

Find the sum: (-3)/(-11)+ (5/9)

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+ 2/3 +4/9 +............

Find the number of divisors of the number N=2^3 .3^5 .5^7 .7^9 which are perfect squares.

Without actually calculating the cubes , find the value of the following. (-12)^(3)+(7)^(3)+(5)^(3)

A two digit number is obtained by either multiplying the sum of digits by 8 and then subtracting 5 or by multiplying the difference of digits by 16 and adding 3. Find the number.

Find the sum : (a) (-7)+ (-9) + 4 + 16

Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number, the variance of the numbers so obtained is :

Using the property of determinants and without expanding prove that {:|( 2,7,65),( 3,8,75),( 5,9,86) |:} = 0