class 11

Math

Algebra

Sequences and Series

The sum of the series $2!1 −3!1 +4!1 −…$ upto infinity is

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Find the sum of the sequence 7, 77, 777, 7777, . . . to n terms.

Find the sum of :(i) the first 1000 positive integers(ii) the first n positive integers

In a factory, 150 workers were engaged to finish a piece of work in a certain number of days. However, if 4 workers are dropped everyday, except the first day, it will take 8 more days to finish the work. Find the number of days in which the work was to be completed.

Check whether 301 is a term of the list of numbers 5, 11, 17, 23, . . .

The $p_{th},q_{th}$and $r_{th}$terms of an A.P. are a, b, c, respectively. Show that $(q−r)a+(r−p)b+(p−q)c=0$.

Find the sum to n terms of the series : 3xx8+6xx11+9xx14+........

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is then sum?

Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.