`(n)/(2)-(3n)/(4)+(5n)/(6)=21`

Solve the linear equations. n/2 - (3 n)/4 + (5 n)/6 = 21

Simplify: (2)/(3)m-(4)/(5)n+(3)/(5)p+(-(3)/(4)m-(5)/(2)n+(2)/(3)p)+((5)/(2)m+(3)/(4)p-(5)/(6)n)

Solve the following linear equations. frac(n)(2) - frac(3n)(4) + frac(5n)(6) = 21

The sum of the series 1+4+3+6+5+8+ upto n term when n is an even number (n^(2)+n)/(4) 2.(n^(2)+3n)/(2) 3.(n^(2)+1)/(4) 4.(n(n-1))/(4)(n^(2)+3n)/(4)

Prove that by using the principle of mathematical induction for all n in N : (1)/(2.5)+ (1)/(5.8) + (1)/(8.11)+ ...+(1)/((3n-1)(3n+2))= (n)/(6n+4)

Prove that by using the principle of mathematical induction for all n in N : (1)/(2.5)+ (1)/(5.8) + (1)/(8.11)+ ...+(1)/((3n-1)(3n+2))= (n)/(6n+4)

(1^(4))/(1.3)+(2^(4))/(3.5)+(3^(4))/(5.7)+......+(n^(4)) /((2n-1)(2n+1))=(n(4n^(2)+6n+5))/(48)+(n)/(16(2n+1))

(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+... n terms =(A)(n)/(6n+4) (B) (n)/(3n+2)(C)(n)/(4n+6)(D)(1)/(2(2n+3))

Prove that 7^(n)(1+(n)/(7)+(n(n-1))/(7.14)+(n(n-1)(n-2))/(7.14.21)...)=4^(n)(1+(n)/(2)+(n(n+1))/(2.4)+(n(n+1)(n+2))/(2.4.6)...)

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+...+(1)/((3n-1)(3n+2))=(n)/((6n+4))=(n)/((6n+4))