H2 Maths - Summation Of Series

chocolates-xed SG

need help and explanation of these questions

1. a series S is given by 1 + (1 + 2) + (1 + 2 + 3) + ... + (1 + 2 + 3 + ... + n). State the rth term of the series S and simplify it. By expressing S in sigma notation, obtain the sum.

ans: n(n+1)(n+2)/6

wee_ws SG

Hi,

Can you see that the rth term is a sum of r terms, i.e. sigma i (i varies from 1 to r)?

Then the rth term is r(r + 1)/2 yes?

Now, the required sum S = sigma r(r + 1)/2 (r varies from 1 to n). You will need this result:

sigma r^2 (r varies from 1 to n) = n(n + 1)(2n + 1) / 6

to obtain the final answer.

Thanks!

Cheers,
Wen Shih

chocolates-xed SG

ok thanks(: