Ineed ..
proof it by mathematical induction
10+24+38++(14n-4)=7n²+3n

When proving something by induction, we have to establish a base case: we must prove that our assumption

is true for . We have

With the base case covered, we assume and prove that if holds, then follows. We have

Rewrite this expression as

Rearrange the terms as follows:

We already know (because we are assuming ) that

And when writing we wrote this equation, adding to both sides.

Recapping, we have assumed that , i.e. we have assumed that

Then we showed that can be written as

And so, if is true, must be true as well. This concludes the proof.

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11