Question

PLEASE HELP WILL GIVE MEDAL! Suppose in a proof of a summation formula 1+5+25+...+5^k -1=1/4 (5^k -1) by mathematical induction, you show the formula valid for L=1 and assume that it is valid for L=k. What is the next equation in the induction step of this proof?
a 1+5+25+...+5^k-1 +5^k+1-1 = 1/4(5^k -1) +1/4(5^k+1 -1)
b 1+5+25+...+5^k +5^k+1 = 1/4(5^k -1)+5^k+1-1
c 1+5+25+...+5^k-1 +5^k+1-1 =1/4 (5^k -1) + 5^k+1-1
d 1+5+25+...+5^k-1 +5^k+1-1 = 1/4 (5^k+1 -1) + 5^k+1-1

Answer 1

add the next kth term to each side maybe?

Answer 2

what do you mean?

Answer 3

well, you need to know if its true for (k+1) terms, and you know its true for (k) terms

soo add the next term to each side ....

Answer 4

in other words:

P(k) = format(k)

P(k) + (k+1) = format(k) + (k+1)

Answer 5

so would it be B because it has 5^k + 5^k+1 ?

Answer 6

it hard to tell, but i think B is good on the right, but bad on the left

Answer 7

1+5+25+...+ 5^k-1 = 1/4 (5^k-1)
^^^^^
let k = k+1



1+5+25+...+ 5^k-1 + 5^k+1-1 = 1/4 (5^k-1) + 5^k+1-1

Answer 8

I see! Thank you so much!!

Answer 9

youre welcome