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3^(2n+2)-8n-9 divisible by 8...

`3^(2n+2)-8n-9` divisible by `8`

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Prove the following by using the principle of mathematical induction for all n in Nvdots3^(2n+2)-8n-9 is divisible by 8.

For every natural number n, 3 ^(2n+2)-8n -9 is divisible by 8

Statement 1:3^(2n+2)-8n-9 is divisible by 64,AA n in N. Statement 2:(1+x)^(n)-nx-1 is divisible by x^(2),AA n in N

Using binomial theorem,prove that 3^(2n+2)-8^(n)-9 is divisible by 64, where n in N.

Prove the following by the principle of mathematical induction: 3^(2n+2)-8n-9 is divisible 8 for all n in N.

Show that 9^(n+1)-8n-9 is divisible by 64, where n is a positive integer.

CBSE COMPLEMENTARY MATERIAL-BINOMIAL THEOREM -SHORT ANSWER TYPE QUESTIONS (section-C)
  1. If the first three terms in the expansion of (a + b)^(n) are 27, 54 an...

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  2. In (3x^(2)-(1)/(x))^(16) which term contains x^(12) .

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  3. Find the term independent of x in the expansion of (a) (sqrt(x/3)+sqrt...

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  4. Evaluate (sqrt2+1)^(5))-(sqrt2-1)^(5) using binomial theorem.

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  5. In the expansion of (1 + x^(2) )^(8) , find the difference between the...

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  6. Find the coefficients of x^(4) in (1 - x)^(2) (2 + x)^(5) using binomi...

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  7. 3^(2n+2)-8n-9 divisible by 8

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  8. If the term free from x in the expansion of (sqrt(x)-k/(x^2))^(10) is ...

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  9. Find the number of integral terms in the expansion of (5^(1/2)+7^(1/8)...

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  10. Given positive integers r>1,n> 2, n being even and the coefficient of...

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  11. If in any binomial expansion a, b, c and d be the 6th, 7th, 8th and 9t...

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  12. If in the expansion of (1+x)^n the coefficient of three consecutive te...

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  13. Show that 2^(4n+4)-15n-16, where n in N is divisible by 225.

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  14. If the coefficients of three consecutive terms in the expansion of (1 ...

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  15. Show that the coefficient of middle term in the expansion of (1 + x)^(...

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  16. If the coefficients of (2r + 4)th and (r - 2)th terms in the expansion...

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  17. Prove that there is no term involving x^(6) is the expansion of (2x^(2...

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  18. The coefficient of three consecutive terms in the expansion of (1 + x)...

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