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Syllabus

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

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

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

2^5n>3^3n for n belongs to natural no.

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

prove by PMI

5+15+45....+5.3

^{n-1}= 5/2(3^{n-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?Prove that n(n+1)(n+5) is a multiple of 3

solve this equation :-

4k

^{3}+ 18k^{2}+ 23k + 9 =0 (step by step)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.

1.2 + 2.2

^{2}+ 3.2^{2}+ … +n.2^{n}= (n– 1) 2^{n}^{+1}+ 2this question is solved on this site...... but I can't understand how the final answer came ..... please see 4.1's 8th question on this site ......

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 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.Please help me I can't solve questions of mathematical induction.I tried a lot but I always get confused in the (k+1)th step.Please tell what to do?

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

Prove that 11

^{n+2 }+ 12^{2n+1 }is divisible by 133 for all n belongs to N .Prove: 5

^{2n}-1 is divisible by 24 for all n NUsing PMI, prove that

5

^{2n+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, 1

^{2}+ 2^{2}+....+ n^{2}(n^{3}/3) for all n belonging to natural numbers= 9

^{(}^{k}^{ + 1) }(8 + 1)= 8. 9

^{(}^{k}^{ + 1)}+ 9^{(}^{k}^{ + 1)}can anyone explain me 2 step how it came...please it is of example no 1.

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 k

^{3}+6k^{2}+9k+4??bY PMI prove n(n+1)(2n+1) is divisible by 6

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

P.T by principle of mathematical induction

Prove that 2.7

^{n}+ 3.5^{n}-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)

^{5}/5+n^{3}/3+7n/15 is a natural number by using the 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 + â€¦â€¦.. + 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 n

^{2}+ n is even , where n is natural number.?To prove 2

^{k }^{+ 1}> (k+ 1)^{ 2 }, we only need to prove that 2k^{2 }> (k+ 1)^{ 2}- why? because 2k

^{2}not equal to 2^{ k+1}pl explain

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

8. 9

^{(}^{k}^{ + 1)}+ 9^{(}^{k}^{ + 1)}âˆ’ 8k âˆ’ 8 âˆ’ 9= {9

^{(}^{k}^{ + 1)}âˆ’ 8k âˆ’ 9} + 8 (9^{(}^{k}^{ + 1) }âˆ’ 1)= 8

m+ 8 (9^{(}^{k}^{ + 1) }âˆ’ 1)= 8{

m+ (9^{(}^{k}^{ + 1) }âˆ’ 1)}plz explain the steps with reasonshttps://www.meritnation.com/discuss/question/1168811/q-using-the-principle-of-mathematical-induction-prove-that-n55-n33-7n15-is-a-natural-number-v-nen

here, i did not understand how 7

^{k+1}/ 15 has been split.......Also right Q :

Q. Using the principle of mathematical induction, prove that n

^{5}/5 + n^{3}/3 + 7n/15 is a natural number~~V~~n E N.1/2*5+ 1/5*8 + 1/8*11 +.......................+

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

= n/6n+4

prove by PMI

Prove that

^{ 1}/_{2 }tan (^{x}/_{2})+^{1}/_{4}tan(^{x}/_{4})+...+(^{1}/_{2n})tan (^{x}/_{2n})=(^{1}/_{2n})cot(^{x}/_{2}^{n}) - cotx for all n (- N and 0<x<(^{pi}/_{2}).prove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nENin 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

^{o}C and 300^{o}C.n

^{7}/7 + n^{5}/5 + 2n^{3}/3 - n/105 is an integer , 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.

Prove the following by the PMI :

n7/ 7 + n5 / 5 + n3 / 3 + n2/ 2 - 37/210n is a positive integer for all n belongs to N.

1+4+7+---------+(3n-2)=

1n(3n-1)2

Using the principle of mathematical induction, prove each of the following for all n belonging to N:

1/2.5+1/5.8+1/8.11 +.... + 1/(3n-1)(3n+2) = n/(6n+4)

Using the principle of mathematical induction, prove each of the following foe all n belonging to N :

(1+1) (1+1/2) (1+1/3) ...(1+1/n) = (n+1)

Prove by PMI

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

URGENT

prove the following by mathematical induction:-41

^{n }-14^{n}is a multiple of 27can anyone tell me how to solve (k+1){1/3k(4k+11)+2(2k+5)}

i dont understand why the next step is 1/3(k+1) {4k

^{2}+23k + 30}11 power n+2 + 12 power 2n+1 is divisible by 133

^{2}-1) is divisible by 24 where n is an odd number greater than 2.^{n-1}a) = sin 2^{n}a / 2^{n}sin aProve by induction that (2n+7)<(n+3)

^{2}is true7 divides 2

^{3n}-1x

^{n}-y^{n }is divisible by x-y

using mathematical induction prove that

n(n+1)(n+2) is divisible by 6.what is principle of mathamatical induction

${1}^{2}+{2}^{2}+{3}^{2}+....+{n}^{2}=\frac{n\left(n+1\right)\left(2n+1\right)}{6}$

7

^{n}-3^{n}is a divisible by 4.please solve this

PROVE BY M.I (41)

^{n}-(14) is multiple of 27Prove the following by using the principle of mathematical induction for all

(2

n+7) < (n+ 3)^{2 }can any pls explain this question in detail??? cuz i can't get it

prove that 2

^{n}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.