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sinx+sin2x+sin3x+...+sin nx=sin((n+1)/2)x .((sin nx)/2) / sin(x/2)
prove by using PMI that 4 raise to n + 15n - 1 is divisible by 9 .
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
1 sqare + 2 square + 3 square +.............+n square >n cube +3 . prove it by mathematical induction.
Prove that n(n+1)(n+2) is divisible by 6
Prove that 2.7n + 3.5n - 5 is divisible by 24 for all n belongs to N. [ please explain with steps]
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.
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
bY PMI prove n(n+1)(2n+1) is divisible by 6
find the equation of parabola whose focus is (1,1) and tangent at the vertex is x + y = 1
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
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??
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)
1/2x5 + 1/5x8 + 1/8x11 + ....................+ 1/(3n-1)(3n+2) = n / 6n+4
using mathematical induction
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.?
3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)
P.T by principle of mathematical induction
1/2*5+ 1/5*8 + 1/8*11 +.......................+
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
prove by ibduction that the sum Sn=n3+3n2+5n+3 is divisible by 3 for all nEN
By using principle of mathematical induction, prove that for all n element of N:
3^2n+2 - 8n - 9 is divisible by 64.
n(n+1)(n+5) is divisible by 6 for all n belongs to natural numbers
prove that 1x2 + 2x2^2 + 3x2^3+..+nx2^n = (n-1)x2^n+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 200oC and 300oC.
9n - 8n -1 is a multiple of 8
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).
n3 - n is divisible by 6, for each natural number n >= 2
Prove by induction that (2n+7)<(n+3)2is true
7 divides 23n-1
using mathematical induction prove that n(n+1)(n+2) is divisible by 6.
why do we apply mode to tan theta= m2-m1/1+m1m2 ? tan theta can itself get both positive and negative values. what is the use of this modulus? not also here but it has been applied to many other cases
what is principle of mathamatical induction
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.
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