Related InterviewSolutions

• `(2n+7) lt (n+3)^(2)`
• If `P(n):2nltn!,ninN` then P(n) is true for all `n≥` . . . . . . . . . .
• Using principle of mathematical induction, prove that `7^(4^(n)) -1` is divisible by `2^(2n+3)` for any natural number n.
• For every positive integer n, prove that `7^n-3^n`is divisible by 4.
• What is the total number of proper subsets of a set containing n elements?
• Prove that `n^5/5 + n^3/3+(7n)/(15)` is a natural number.
• Using the principle of mathematical induction, prove each of the following for all `n in N` `3^(n) ge 2^(n)`
• `1+3+3^(2)+…….+3^(n-1) =((3^(n)-1))/(2)`
• Prove that `1/(n+1)+1/(n+2)+...+1/(2n)> 13/24` ,for all natural number `n>1`.
• `1+1/(1+2)+1/(1+2+3)+1/(1+2+3+n)=(2n)/(n+1)`