Please solve last 2 question in detail Q 13 Show that 9n+1-8n-9 is divisible by 64, whenever n - Maths - Binomial Theorem

Question

Please solve last 2 question in detail
Q 13 Show that 9 n + 1 - 8 n - 9 is divisible by 64, whenever n is
a positive integer
Q 14 Prove that ∑ r = 0 n 3 r   C r n = 4 n

Ankita Agarwal · Accepted Answer

Dear Student,

Refer the link for the answer to your query:

Q 13 
https://www meritnation
com/ask-answer/question/using-binomial-theoram-show-that-9n-1-8n-9-is-divisible-by-6/binomial-theorem/3767333

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Please solve last 2 question in detail. Q.13. Show that 9 n + 1 - 8 n - 9 is divisible by 64, whenever n is a positive integer. Q.14. Prove that ∑ r = 0 n 3 r C r n = 4 n .

Please solve last 2 question in detail.
Q.13. Show that $9^{n + 1} - 8 n - 9$ is divisible by 64, whenever n is a positive integer.
Q.14. Prove that $\sum_{r = 0}^{n} 3^{r} {}^{n}C_{r} = 4^{n}$ .