Manhattan Advanced quant strategy

[prachibansal89]

On page 143 of manhattan advanced quant,
Ques : if nth term is 1/n(n+1), we need to find summation A100.
By finding the first few terms, the book derives the formula for summation of 100 terms.
Can someone please tell me how to derive this formula without plugging in the values? It would be a useful technique to calculate the formulas quickly instead of having to plug the values and then try and derive the formula from there.

Thanks!

[StaceyKoprince]

Please remember to read (and follow!) the forum guidelines before posting. This folder is only for general strategy questions, not content or specific test problems. Check out the content / problem folders and post in the relevant folder depending upon the source of the problem you want to post (and make sure to follow the rules about banned sources). If you are a course student, you can also ask about other problems or issues before or after class or during section.

In this case, your question would go in the MGMAT non-CAT folder.

I'll give you a short answer here but if you want to discuss in more detail (or ask additional questions), please post in the relevant folder. Thanks!

In the case of a problem like this, you really do have to find the pattern. The formula is not a standard formula - they're giving you a unique formula and you just have to find the pattern.

Usually, you only need to find about 4 terms in order to find the pattern!