Question
Download Solution PDFHow many terms are there in the expansion of \(\rm \left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)^{21}\) where a ≠ 0, b ≠ 0?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
If a and b are real numbers and n is a positive integer, then
(a + b)n = nC0 an + nC1 an - 1 b1 + ......... nCn bn for \(\rm 0 \leq r \leq n\)
Total number of terms in (a + b)n = n + 1
Calculation:
We have to find the total number of terms in \(\rm \left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)^{21}\) where a ≠ 0, b ≠ 0
⇒ \([{\rm \left(\frac{a}{b}+\frac{b}{a}\right)^{2}}]^{21}\)
⇒ \({\rm \left(\frac{a}{b}+\frac{b}{a}\right)^{42}}\)
∴ The total number of terms in the expression is 42 + 1 = 43.
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