Related InterviewSolutions

• prove that `7 + 77 + 777 +...... + 777........._(n-digits) 7 = 7/81 (10^(n+1) - 9n - 10)` for all `n in N`A. a=1,b=9,c=9B. a=1,b=9,c=10C. a=1,b=-9,c=-10D. a=1,b=-9,c=-10
• Statement-1: `cos10^(@)+cos20^(@)+…..+cos170^(@)=0` Statement-2: `cos alpha+cos(alpha+beta)+....+cos(alpha+(n-1)beta)=(cos(alpha+((n-1)beta)/(2))sin((nbeta)/(2)))/(sin((beta)/(2))), beta ne 2npi.`
• Statement-1: For every natural number `n ge 2, (1)/(sqrt1)+(1)/(sqrt2)+…..(1)/(sqrtn) gt sqrtn` Statement-2: For every natural number `n ge 2, sqrt(n(n+1) lt n+1`
• Statement-1: `sin10^(@)+sin120^(@)+....+sin350^(@)=0` Statement-2: `sin alpha+sin (alpha+beta)+....+sin(alpha+(n-1)beta)=(sin(alpha+((n-1)beta)/(2))sin((nbeta)/(2)))/(sin((beta)/(2))), beta ne 2npi.`
• Statement-1: The sum of n terms of the series `a+(a+d)+(a+2d)+...(a+(n-1)d)=(n)/(2)[2n+(n-1)d]` Statement-2:- Mathematical induction is valid only for natural numbers.
• Most of the formulae are verified on the basis of induction method by putting n=1,2,…. `27^(n)-8^(n)` is divisible by `("for "n in N)`.A. `3^(n)-2^(n)`B. `3^(n)+2^(n)`C. `4^(n)-3^(n)`D. `4^(n)+3^(n)`
• Statement-1: sin`(pi+theta)=-sin theta` Statement-2: `sin(npi+theta)=(-1)^(n) sin theta`, `n in N`.
• Statement-1: `n(n+1)(n+2)` is always divisible by 6 for all `n in N`. Statement-2: The product of any two consecutive natural number is divisible by 2.
• Statement-1: `7^(n)-3^(n)` is divisible by 4. Statement-2: `7^(n)=(4+3)^(n)`.
• Statement-1: `1^(2)+2^(2)+....+n^(2)=(n(n+1)(2n+1))/(6)"for all "n in N` Statement-2: `1+2+3....+n=(n(n+1))/(2),"for all"n in N`