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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?solve this equation :-

4k

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

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 ......

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 .= 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.

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

P.T by principle of mathematical induction

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

~~V~~nEN.5+15+45+....+5.3

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

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.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.?9n - 8n -1 is a multiple of 8

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

Prove the following by using the principle of mathematical induction for all n belongs to N

1+2+3+.......+n2 plzzzzzzzzz explain in the simplest way as possible

1.2+2.2^2+3.2^3+....+n.2^n=(n -1 )2 n+3

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

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

= n/6n+4

prove by PMI

there are total 50 ques in ex12.2 of r.d sharma, ch. mathematical induction

but meritnation has provided only solutions to 37 ques

certain ques are missing from in between

kindly rectify this problem.

regards

prove by ibduction that the sum Sn=n

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

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)=

1n(3n-1)2

1 sq+2sq+3sq+4sq+......+n sq =n(n+1)(2n+1)/6.

please do the calculations in simplest way with details and please no links

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

^{o}C and 300^{o}C.11 power n+2 + 12 power 2n+1 is divisible by 133

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 induction that (2n+7)<(n+3)

^{2}is truepls someone explain how to prove the problems in this chapter ! its so confusing especially the last 3-4 steps ! :(( !

rnrevision notes or tips ..... pls reply

7 divides 2

^{3n}-1prove dt ....

3

^{4n+2}+ 5^{2n+1 is a multiple of 14}using mathematical induction prove that

n(n+1)(n+2) is divisible by 6.1 sqare + 2 square + 3 square +.............+n square >n cube +3 . prove it by mathematical induction.

what is principle of mathamatical induction

7

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

(X2n -1) is divisible by (X-1)

its actually X raise to the power 2n

PROVE BY M.I (41)

^{n}-(14) is multiple of 271. 2.7

^{n}+ 3.5^{n}-5 is divisible by 24,n belongs to natural number2. 3

^{2n-2}-8n-9 is divisible by 8 ,n belongs to natural numberProve 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

using PMI prove that 3 to the power (2n-1) is divisible by 8 where n belongs to N.

plz reply

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.

1/1.2 + 1/2.3 = 1/3.4 +.........+ 1/n(n+1 )= n/n+1 using principle of mathematical induction