" 418"1+2+2^(2)+2^(3)+.........+2^(n-1)=255," #tl "n" all "EE17" sitil "

If 1+2+2^(2)+...+2^(n-1)=255 then find n

If the sum of 1+2+2^(2)+ . . . . . . . . . .+2^(n-1) is 255, find the value of n.

Prove that : (2n) ! = 2^n (n!)[1.3.5.... (2n-1)] for all natural numbers n.

For all n gt 1 , prove that 1^(2)+2^(2)+3^(2)+4^(2)+...........+n^(2) = (n(n+1)(2 n+1))/(6)

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

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

Prove that by using the principle of mathematical induction for all n in N : 1.2+ 2.2^(2)+ 3.2^(3)+ ....+ n.2^(n)= (n-1)2^(n+1)+2

Prove that by using the principle of mathematical induction for all n in N : 1.2+ 2,2^(2)+ 3.2^(3)+ ....+ n.2^(n)= (n-1)2^(n+1)+2

Prove that by using the principle of mathematical induction for all n in N : 1.2+ 2.2^(2)+ 3.2^(3)+ ....+ n.2^(n)= (n-1)2^(n+1)+2

If the sum 1+2+2^2+......+2^(n-1) is 255, then find the number of terms.