Please help me do this question.

Find the last five digits of

(101^{^100) }-1

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- May 27th 2012, 12:14 PMaakgoelFind the Last Five Digits
Please help me do this question.

Find the last five digits of

(101^{^100) }-1 - May 28th 2012, 12:26 AMBobPRe: Find the Last Five Digits
10000

Use the binomial expansion for $\displaystyle (1+100)^{100}.$ - May 30th 2012, 05:41 AMaakgoelRe: Find the Last Five Digits
Dear Sir thank you for your consideration.

But how would the binomial expansion of the same help as then I would have to add all the numbers

and then get my results.

Please help and give a proper explanation if possible.

Regards

aakgoel - May 30th 2012, 05:57 AMemakarovRe: Find the Last Five Digits
$\displaystyle (1 + 100)^{100} - 1 = \binom{100}{1}100+\binom{100}{2}100^2+\binom{100}{ 3}100^3+\dots$. All terms starting from the third one end with at least 6 zeros, so you need to consider the first two terms only.