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Using binomial theorem, find the value o...

Using binomial theorem, find the value of `(0.99)^(15)` up to four places of decimal.

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Verified by Experts

We have
`(0.99)^(15)=(1-0.01)^(15)`
`=1-.^(15)C_(1) xx(0.01) + .^(15)C_(2) xx (0.01)^(2)-.^(15)C_(3) xx (0.01)^(3) +...`
[neglecting higher powers of 0.01]
`=1-15 xx(0.01) + 105 xx (0.0001)-455 xx (0.000001)+...`
`=1-0.15+0.0105 + 0.000455 = 0.860045.`
Hence, `(0.99)^(15) = 0.860045.`
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RS AGGARWAL-BINOMIAL THEOREM-EXERCISE 10B
  1. Using binomial theorem, find the value of (0.99)^(15) up to four place...

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  2. Show that the term independent of x in the expansion of (x-1/x)^(10) ...

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  3. If the coefficents of x^(2) and x^(3) in the expansion of (3+px)^(9)...

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  4. Show that coefficient of x^(-3) in the expansion of (x-1/x)^(11) is -3...

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  5. Show that the middle term in the expansion of ((2x^2)/3+3/(2x)^(2))^(1...

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  6. Show that the coefficient of x^(4) in the expansion of (x/2-3/x^(2))^(...

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

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  8. Show that the coefficient of x^(4) in the expansion of (1+2x+x^(2))^(5...

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  9. Write the number of terms in the expansion of (sqrt(2)+1)^(5)+ (sqrt(...

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  10. Which term is independent of x in the expansion of (x-1/(3x^(2)))^(9)?

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  11. Write the coefficient of the middle term in the expansion of (1+x)^(2...

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  12. Write the coefficient of x^(7) y^(2) in the expansion of (x+2y)^(9).

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  13. If the coefficent of (r-5)th and (2r-1)th terms in the expansion of (...

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  14. Write the 4th term form the end in the expansion of (3/(x^(2))-x^(3)/6...

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  15. Find the coefficient of x^n in the expansion of (1+x)(1+x)^ndot

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  16. In the binomial expansion of (a+b)^n , coefficients of the fourth and ...

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  17. Find a positive value of m for which the coefficient of x^2 in the ex...

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