Page:Elementary algebra (1896).djvu/17

CONTENTS. xiii CHAPTER PAGE Advantages of Common Logarithms 355 Logarithms transformed from Base a to Base b 357 Logarithms in Arithmetical Calculation 358 Four-Place Table of Logarithms 360 Use of the Table 362 Cologarithms 365 Exponential Equations 366

XXXIX. Interest and Annuities 367

XL. Limiting Values and Vanishing Fractions 370

XLI. Convergency and Divergency of Series 377 Tests for Convergency 377 Auxiliary Series 383

XLII. Undetermined Coefficients 386 Functions of Finite Dimensions 386 Functions of Infinite Dimensions 390 Expansion of Fractions into Series 391 Expansion of Surds into Series 392 Reversion of Series 393 Partial Fractions 394 The General Term 397

XLIII. Continued Fractions 400 Formation of Successive Convergents 403 Limits to Error 407 Recurring Continued Fractions 409

XLIV. Summation of Series 413 Scale of Relation 413 The Sum of n Terms 415 The General Term 417 The Method of Differences 418 Any Required Term 419 The Sum of n Terms 420 Piles of Shot and Shells 422 Interpolation 425

XLV. Binomial Theorem: Proof for Any Index 426

XLVI. Exponential and Logarithmic Series 430