Hi guys, here are some basic formulas in series.

**DOWNLOAD READ & PRINT – Basic formulas in series (pdf)**

**Basic formulas in series**

**Arithmetic series**

is an arithmetic series.

Here

Thus th term is

Sum of first terms of the series is

**Geometric series**

is a geometric series.

Here

Thus th term is

Sum of first terms of the series is

For

**Powers of natural numbers**

For

For

For

**Infinite series**

Any infinite series looks like

This series will be convergent if

This series will be divergent if

### Test for convergence

**Test 1**

a)

b)

**Test 2: Comparison test**

It is useful for standard series like

For the series is convergent.

For the series is divergent.

**Test 3: D’ Alembert’s ratio test for positive terms**

a)

b)

c)

**Test 4: For general series:**

a) If converges, is absolutely convergent.

b) If diverges but converges, is conditionally convergent.

## Leave a Reply