Q3 of 60 Page 21

Write the sum to n terms of a series whose rth term is: r + 2^r

The general term be = i + 2ⁱ

= Sum of series

We know by property that:

∑axⁿ + bx^{n - 1} + cx^{n - 2}…….d₀=a∑xⁿ + b∑x^{n - 1} + c∑x^{n - 2}…….. + d₀∑1

Thus

Substituting the above value

Thus

Write the sum of the series : 2 + 4 + 6 + 8 + ….. + 2n

Write the sum of the series : 1² – 2² + 3² – 4² + 5² – 6² + ……. + (2n – 1)² – (2n)²

If , find .

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then write the value of k.

Questions · 60

21. Some Special Series

1 2 3 4 5 6 7 8 8 8 8 9 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10

Write the sum to n terms of a series whose rth term is: r + 2r