12 +2^2 +3^2 +4^2 +5^2 +...+n^2 = n (n+^16 ) (^2 n+^1 )
where ‘n’ is the number of terms in the sequence.
- Sum of the cubes of the first ‘n’ natural numbers
The sum of the first ‘n’ natural numbers can be found by the formula,
13 +2^3 +3^3 +4^3 +5^3 +...+n^3 =
()^2
2
n n 1
⎭⎬
⎫
⎩⎨
⎧ + where ‘n’ is the number of terms in the sequence.
Memorisation of mathematical formula is inevitable. However, the child be assisted
to understand it first. Spatial presentation of this on braille paper is necessary to
enable the child to explore and understand.
- Synthetic division
Synthetic division is the simplified form of ordinary division. In synthetic division
the coefficients are taken separately and then divided by the constant in the binomial.
Eg: Divide x^2 + 5x + 6 by x – 2
2156
0214
1720
Quotient = x + 7 Remainder = 20
Detach the coefficients 1, 5 and 6 from the quadratic expression x2 + 5x + 6 and write
them in order horizontally. Since the diviser is x – 2 the coefficients must be divided
by 2. (Please note that the sign of the constant in the divisor is changed). Note that
unlike normal division where the products are subtracted, in synthetic division the
products are to be added. Also as a common rule, in the first step, zero is to be added
with the first coefficient. Thus write 2 to the left of the coefficients and then add
zero with the first coefficient ‘ 1 ’. The sum is 1. Now multiply 1 with the divisor 2.
