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 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

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 .

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

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

 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

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

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

 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

 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??

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

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.....

Prove by induction:

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

p(n) =1+4+7+...+(3n-2)=1/2n(3n-1)

P.T by principle of mathematical induction

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

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

Prove by using principle of mathematical induction :cos a+ cos (a+b)+ cos (a+2b)+......+cos [a+(n-1)b] = {cos [a+ ((n-1)/2)b]sin (nb/2)}/sin (b/2)

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

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

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

= n/6n+4

prove by PMI

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

prove that the product of two consecutive natural numbers is an even umber using the principal of mathematical induction

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

Prove by PMI

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

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 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).

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

solve this equation :-

4k³+ 18k² + 23k + 9 =0 (step by step)

7 divides 2³ⁿ-1

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

for every positive integer n, prove that 7^n- 3^n is divisible by 4 plz expertz explain me how to solve dis step by step

what is principle of mathamatical induction

prove that 1x2 + 2x2^2 + 3x2^3+..+nx2^n = (n-1)x2^n+1 +2

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

prove that 2ⁿ is greater than n for all positive integers n.

this is example 2 from the ncert maths text book.

plzz...answer soon....i dint get the last step.