साबित करें कि (2^n + 2^(n-1))/(2^(n+1) - 2^n) = 3/2

(2^(n)+2^(n-1))/(2^(n+1)-2n)=(3)/(2)

Prove that (2^(n)+2^(n-1))/(2^(n+1)-2^(n))=(3)/(2)

[ If 2 is the sum of infinity of a G.P.,whose first clement is 1 ,then the sum of the first n terms is [ 1) (2^(n)-1)/(2^(n)), 2) (2^(n)-1)/(2^(n-1)), 3) (2^(n-1)-2)/(2), 4) (2^(n-1)-1)/(2^(n))]]

show that (3*2^(n+1)+2^(n))/(2^(n+2)-2^(n-1))=2

(2.3^(n+1)+7.3^(n-1))/(3^(n+1)-2((1)/(3))^(1-n))=

lim_(n rarr oo)(3^(n+1)+2^(n+2))/(3^(n-1)+2^(n-2)) =

1+2.2+3.2^(2)+4.2^(3)+...+n*2^(n-1) = (i) 1+ (1+n) 2^(n) (ii) 1- (1+n) 2^(n) (iii) 1- (1-n) 2^(n) (iv) 1+ (1-n) 2^(n)

Evaluate : (a^(2n+1) xx a^((2n+1)(2n-1)))/(a^(n(4n-1)) xx (a^2)^(2n+3)

lim_ (n rarr oo) [(1) / (n) + (n ^ (2)) / ((n + 1) ^ (3)) + (n ^ (2)) / ((n + 2) ^ (3)) + ...... + (1) / (8n)]

2C_0 + 2^2 (C_1)/(2) + 2^3 (C_2)/(3) + ………. + 2^(n+1) (C_n)/(n+1) = (3^(n+1) - 1)/(n+1)