- Home
- Standard 11
- Mathematics
7.Binomial Theorem
medium
${C_1} + 2{C_2} + 3{C_3} + 4{C_4} + .... + n{C_n} = $
A
${2^n}$
B
$n.\,\,{2^n}$
C
$n.\,\,{2^{n - 1}}$
D
$n.\,\,{2^{n + 1}}$
Solution
(c) Trick : Put $n = 1,\,\,2,\,\,3,….$
${S_1} = 1,\,\,{S_2} = 2 + 2 = 4$
Now by alternate $(c)$, put $n = 1,\,\,2$
${S_1} = {1.2^0} = 1,{S_2} = {2.2^1} = 4$
Standard 11
Mathematics