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)
1^4+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
find the equation of parabola whose focus is (1,1) and tangent at the vertex is x + y = 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 x2n-y2n is divisible by x+y?
1 sqare + 2 square + 3 square +.............+n square >n cube +3 . prove it by mathematical induction.
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
Prove 22202n+1+20032n+1is divisible by 4005,n belongs to N
using induction, prove that 10n + 3.4n+2 + 5 is divisible by 9
Q. If P(n) is statement "n2-n+41 is a prime number"' show that P(1),P(2) are true but P(41) is not true.
Prove that 11n+2 + 122n+1 is divisible by 133 for all n belongs to N .
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