Explain, both mathematically and verbally, why the following are true. (a) 4 = ^x 4-

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Explain, both mathematically and verbally, why the following are true.

(a) 4 = ^x 4-

(b) 4+« = 4 Px 'Px+\ Px+n-\

\,^) m+nPx ^^ nPx ' mPx+n

(d) qx + Px- qx+] + iPx • qx+2 + • • • =1.

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