First slide

Binomial theorem for positive integral Index

Question

$C_{0} + 4 \cdot C_{1} + 7 . C_{2} + . (n + 1) terms =$

Moderate

A

$(3n+2) 2^{n-1}$
B

$(2n+3) 3^{n-1}$
C

$(2n+3) 2^{n-1}$
D

$(3n+2) 3^{n-1}$

Solution

$\begin{array}{l} (n + 1) th term of 1, 4, 7, \dots is 1 + n (3) = 3 n + 1 . Sum \\ = (3 n + 1 + 1) 2^{n - 1} = (3 n + 2) 2^{n - 1} \end{array}$

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