sinx+sin2x+sin3x+...+sin nx=sin((n+1)/2)x .((sin nx)/2) / sin(x/2)

Prove that 1.2 + 2.3 + 3.4 +..............n(n+1) = 1/3 n (n+1)(n+2)

1^4+2^4+3^4+..........+n^4 =n(n+1)(2n+1)+(3n^2+3n-1)/30. (whole divided by 30)

sinx + sin3x + ..............+ sin(2n-1)x = sin^2 nx / sinx

prove by PMI

find the equation of parabola whose focus is (1,1) and tangent at the vertex is x + y = 1

prove by using PMI that 4 raise to n + 15n - 1 is divisible by 9 .

Prove that 2.7n + 3.5n - 5 is divisible by 24 for all n belongs to N. [ please explain with steps]

Prove that x^{2n}-y^{2n} is divisible by x+y?

1 sqare + 2 square + 3 square +.............+n square >n cube +3 . prove it by mathematical induction.

Prove that n(n+1)(n+5) is a multiple of 3

5+15+45....+5.3^{n-1}= 5/2(3^{n-1})

Prove by PMI

1) a+(a+d)+(a+2d)+ ......[a+(n-1)d] = n/2 [2a+(n-1)d], n E N.

2) n(n+1)(n+5) is divisible by 6 for all n E N.

3) 9 raised to n - 8n - 1 is a multiple of 64 for all n E N.

Prove that n(n+1)(n+2) is divisible by 6

Using PMI Prove that 1^2 + 2^2 + ......... + n^2 n^3/3

Prove 2220^{2n}^{+1}+2003^{2n+1}is divisible by 4005,n belongs to N

using induction, prove that 10^{n }+ 3.4^{n+2} + 5 is divisible by 9

Q. If P(n) is statement "n^{2}-n+41 is a prime number"' show that P(1),P(2) are true but P(41) is not true.

Prove that 11^{n+2 }+ 12^{2n+1 }is divisible by 133 for all n belongs to N .

sinx+sin2x+sin3x+...+sin nx=sin((n+1)/2)x .((sin nx)/2) / sin(x/2)

Prove that 1.2 + 2.3 + 3.4 +..............n(n+1) = 1/3 n (n+1)(n+2)

1^4+2^4+3^4+..........+n^4 =n(n+1)(2n+1)+(3n^2+3n-1)/30. (whole divided by 30)

sinx + sin3x + ..............+ sin(2n-1)x = sin^2 nx / sinx

prove by PMI

find the equation of parabola whose focus is (1,1) and tangent at the vertex is x + y = 1

prove by using PMI that 4 raise to n + 15n - 1 is divisible by 9 .

Prove that 2.7n + 3.5n - 5 is divisible by 24 for all n belongs to N. [ please explain with steps]

^{n+1}- 9n- 10) for all n NProve that x

^{2n}-y^{2n}is divisible by x+y?1 sqare + 2 square + 3 square +.............+n square >n cube +3 . prove it by mathematical induction.

Prove that n(n+1)(n+5) is a multiple of 3

5+15+45....+5.3

^{n-1}= 5/2(3^{n-1})Prove by PMI

1) a+(a+d)+(a+2d)+ ......[a+(n-1)d] = n/2 [2a+(n-1)d], n E N.

2) n(n+1)(n+5) is divisible by 6 for all n E N.

3) 9 raised to n - 8n - 1 is a multiple of 64 for all n E N.

Prove that n(n+1)(n+2) is divisible by 6

Using PMI Prove that 1^2 + 2^2 + ......... + n^2 n^3/3

Prove 2220

^{2n}^{+1}+2003^{2n+1}is divisible by 4005,nbelongs toNusing induction, prove that 10

^{n }+ 3.4^{n+2}+ 5 is divisible by 9^{2n}+ 2^{3n-3}, 3^{n-1}is divisible by 25, for all n Ꜫ N.Q. If P(n) is statement "n

^{2}-n+41 is a prime number"' show that P(1),P(2) are true but P(41) is not true.Prove that 11

^{n+2 }+ 12^{2n+1 }is divisible by 133 for all n belongs to N .