If the fractional part of the number , then k is equal to

Engineering

Mathematics

Application of Binomial Theorem and Summation Of Series

Question

If the fractional part of the number $\frac{2^{403}}{15} is \frac{k}{15}$ , then k is equal to

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$\frac{2^{403}}{15} = \frac{2^{3} . 2^{400}}{15} = \frac{8 . {(1 + 15)}^{100}}{15}$

$= \frac{8 (^{100} C_{0} +^{100} C_{1} (15) +^{100} C_{2} {(15)}^{2} + . ......)}{15}$

$\frac{8}{15} + 8 (^{100} C_{1} (15) +^{100} C_{2} {(15)}^{2} + . ......)$

Remainder is 8.