Prove that: `2xx^7C_4=^8C_4`

Prove that: 3^(1/2)xx3^(1/4)xx3^(1/8)xx...=3

Prove that C_0 + 2.C_1 + 4.C_2 + 8.C_3 + ……+2^n.C_n = 3^n

In DeltaABC , a=9,b=8 and c=4, prove that: cosB-2cosC=-4/3

Prove that .^(n-1)C_(3)+.^(n-1)C_(4) gt .^(n)C_(3) if n gt 7 .

If a ,b ,c are in A.P., prove that: i. (a-c)^2=4(a-b)(b-c) ii. a^2+c^2+4a c=2(a b+b c+c a) iii. a^3+c^3+6a b c=8b^3

Prove that: (1/4)^(-2)-3\ xx\ 8^(2/3)\xx\ 4^0+\ (9/(16))^(-1/2)=(16)/3

With usual notations prove that 2.C_0 + 7.C_1 + 12.C_2 + ……..+(5n + 2).C_n = (5n + 4).2^(n-1)

If A=1/9[-8 1 4 4 4 7 1-8 4] , prove that A^(-1)=A^T .

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2m+1) 2^(n) .

Prove that following i) 2.C_(0)+5.C_(1)+8.C_(2)+…..+(3n+2)C_(n)=(3n+4).2^(n-1)