Ask Question
27 January, 23:43

Find the first 4 terms in the expansion of (1 + x 2) 8. Use your answer to find the value of (1.01) 8

+3
Answers (1)
  1. 28 January, 00:07
    0
    (1+x^2) ^8

    = (1+8x^2+8*7 / (1*2) x^4+8*7*6 / (1*2*3) x^6+8*7*6*5 / (1*2*3*4) x^8 + ...)

    =1+8x^2+28x^4+56x^6+70x^8 + ...)

    For x<1, higher power terms diminish in value, hence we can approximate powers of numbers.

    1.01 = (1+0.1^2) = > x=0.1 in the above expansion

    (1.01) ^8

    =1+8 (0.1^2) + 28 (0.1^4) + 56 (0.1^6) [ limited to four terms, as requested]

    =1+0.08+0.0028+0.000056 (+0.00000070)

    =1.082856 (approximately)
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Find the first 4 terms in the expansion of (1 + x 2) 8. Use your answer to find the value of (1.01) 8 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers