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

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

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

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

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

prove by PMI

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

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

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

Find the multiplicative inverse of (6+5i)²

 Prove that x²ⁿ-y²ⁿ is divisible by x+y?

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

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

7 divides 2³ⁿ-1

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

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

Prove that 11ⁿ⁺² + 12²ⁿ⁺¹ is divisible by 133 for all n belongs to N .

 prove by ibduction that the sum Sn=n³+3n²+5n+3 is divisible by 3 for all nEN

Prove: 5²ⁿ-1 is divisible by 24 for all n N

 Using PMI, prove that 

5²ⁿ⁺²-24n-25 is divisible by 576 for n belongs to N.         

Prove the following

1.3 + 3.5 + 5.7 + ..... +(2n - 1) (2n + 1 ) =n( 4n square + 6n -1)/2 plz explain briefly in a simple method

using principle of mathematical induction prove that, 1² + 2² +....+ n² (n³/3) for all n belonging to natural numbers

 what is P.M.I.    this? EXPLAIN .

 Q. Prove that 1.3+2.4+3.5+....+n(n+2) = 1/6n (n+1) (2n+7),V nEN.

how to split a cubic polynomial like k³+6k²+9k+4??

Prove that 2.7ⁿ + 3.5ⁿ-5 is divisible by 24, for all n belongs to N....Plzzz dnt tell to refer textbook as frm dat also its not clear to me plzzzzzz answer it as soon as possible.....

bY PMI prove n(n+1)(2n+1) is divisible by 6

prove that (1+x)ⁿ >=(1+nx),for all natural number n,where x>-1

Prove by induction:

1/1.2 + 1/2.3 + 1/3.4 + ..... to n terms = n/(n+1)

by PMI prove , 1/1.3 + 1/3.5+ 1/5.7+.......... 1/(2n-1)(2n+1) = n/(2n+1)

using mathematical induction

prove that

7+ 77+ 777+ ..............+ 77.........7 = 7/81 (10to the power n+1 -9n-10)

1 / 1.2.3 + 1 / 2.3.4 + 1 / 3.4.5 + …….. + 1 / n (n+1) (n+2) = n (n+3) / 4 (n+1) (n+2) ? using principle of mathematical induction prove the following for all n E N ?

3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)

Prove that n² + n is even , where n is natural number.?

1/2*5+ 1/5*8 + 1/8*11 +.......................+

1/(3n-1)(3n+2)

= n/6n+4

prove by PMI

Hi

By using principle of mathematical induction, prove that for all n element of N:

3^2n+2 - 8n - 9 is divisible by 64.

1+4+7+---------+(3n-2)=1 n(3n-1) 

                                         2

in drilling worlds deepest hole it was found that the temperature T in degree celcius at x km below the surface of the earth was =30+25(x - 3), 3 less than x less than 15. at what depth will the temperature lie b/w 200^oC and 300^oC.

 11 power n+2   +  12 power 2n+1    is divisible by 133

Prove by induction that (2n+7)<(n+3)²is true

Prove by PMI

n(n+1)(n+5) is divisible by 6 for all n belongs to natural numbers

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

Prove that ¹/₂ tan (^x/₂)+¹/₄tan(^x/₄)+...+(¹/_2ⁿ)tan (^x/_2ⁿ)=(¹/_2ⁿ)cot(^x/_2ⁿ) - cotx for all n (- N and 0<x<(^pi/₂).

what is principle of mathamatical induction

using mathematical induction prove that n(n+1)(n+2) is divisible by 6.

7ⁿ-3ⁿ is a divisible by 4. 

please solve this

PROVE BY M.I (41)ⁿ-(14) is multiple of 27

Prove the following by using the principle of mathematical induction for all

(2n+7) < (n+ 3)²

can any pls explain this question in detail??? cuz i can't get it

by mathematical induction prove that : 

x^2n-1​ -1 is divisible by x-1