Why is the line in bold valid (Picture added below)?

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Answer 1 · 2017-07-22T17:34:29

Refer to the Explanation.

So far, it has been proved, that,

#(1+p)^(k+1) ge 1+kp+p+kp^2....(ast^1).#

Now, note that, #p > -1 rArr p^2 > 0." Also, "k in ZZ^+.#

#:. kp^2 > 0.#

Adding, on both sides of this inequality #1+kp+p,# we get,

# kp^2+1+kp+p > 1+kp+p.............(ast^2).#

Combining, #(ast^1) and (ast^2),# we have,

# (1+p)^(k+1) >= 1+kp+p+p^2 > 1+kp+p, i.e.,#

# (1+p)^(k+1) > 1+(k+1)p.#

In simple form, the line in bold means that,

if, #a >= b+c, &, c >0,# then, if we drop #c >0,# from #b+c,#

we still have, #a > c.#