First slide

Binomial theorem for positive integral Index

Question

The last two digits of the number 3⁴⁰⁰ are

Moderate

A

81
B

43
C

29
D

01

Solution

$\begin{array}{l} 3^{400} = 81^{100} = (1 + 80)^{100} \\ =^{100} C_{0} +^{100} C_{1} 80 + \dots +^{100} C_{100} 80^{100} \end{array}$
Thus, the last two digits are 01 .

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